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]]>Imagine you have an x-y graph with a plotted line running from left to right. In addition to marking these specific data points, you may need to calculate the area of the region under the line. While this is easy enough to do with a straight line, a curving, irregular line is more problematic. This is where the trapezoidal rule comes into play.

The trapezoidal rule creates a series of side-by-side, left-to-right trapezoids under the curve. All the individual trapezoid areas are then added together to calculate the total area under the x-y points making up the curving line. The more trapezoids you use, the more accurate the total area calculated will be.

If you're taking calculus or are an engineer, you likely use the trapezoidal rule on a regular basis. And, while you can solve this by hand, there's no need to because of the free trapezoidal rule calculators and software available to do it for you. We'll go over your best options below.

The first known use of the trapezoidal rule dates to 50 BCE when it was used for integrating Jupiter's velocity on the ecliptic. While other equations such as Simpson's Rule can provide an even more accurate integral – that is, the total area under the graph – the trapezoidal rule is still used for periodic functions and double exponential functions.

In more tangible, real-world applications, the trapezoidal rule is often used in civil engineering:

If you need a free trapezoidal rule calculator, there are websites which will do this for you while providing varying degrees of information. You can also download software to your graphing calculator or computer. Here are your best options.

Wolfram|Alpha's goal is to make systematic knowledge computable and accessible to everyone. This has been made possible over the past thirty years via two means: the Wolfram Language programming code and a New Kind of Science (NKS), the discovery of new algorithms for computation. Designed to be used by students, educators, and researchers, a variety of online and mobile apps are available.

On the trapezoidal rule calculator page, there are four input fields: function, number of trapezoids, lower limit, and upper limit. For example, you could input the following information:

After pressing Submit, you'll get the answer: 0.790821. You will not, however, receive any additional information about how the calculation was performed.

You can share the page via email, Twitter, and Facebook. It's also easy to customize the calculator and embed it on your own webpage, Blogger, or WordPress site. In addition, if you set up an account at Wolfram|Alpha, you can build your own apps through the developer interface.

This site is more basic and less robust in its offerings than Wolfram|Alpha, yet it does provide some additional information of value to students in particular. Once again, to use the trapezoidal rule calculator, you'll be prompted to enter the same four categories of information as above albeit in a slightly different order:

After pressing Submit, you'll get the answer: 1.4753289483117. Unlike Wolfram|Alpha, however, you have the option to see how all the steps were performed in addition to accompanying explanatory information.

Unfortunately, there is no option to embed this calculator on your own site even though you can share it via email or social media. There are also quite a few advertisements which clutter the page's layout.

Based in Russia, PlanetCalc is a collection of more than 550 online calculators. If you need a calculator not on the site, you can submit a detailed request which will be directed to one of its more than 100 volunteer programmers. Any PlanetCalc calculator can also be embedded on your website.

As with the previous online calculators, you'll enter the function, lower and upper limits, and the number of intervals/trapezoids. Unlike them, however, you can adjust the precision of the answer from zero to twenty decimal points. You will also be able to see all the steps performed in the calculation as well as accompanying explanatory notes. Even more helpful, an x-y graph as per your inputted data will be generated so you'll have a visual representation of what you've just calculated.

GeoGebra is another education site with many online apps for everything from geometry to 3D graphing to spreadsheets and more. In addition, many of the apps can be downloaded for iOS, Android, Windows, Mac, Chromebook, and Linux operating systems.

What makes GeoGebra's trapezoidal rule calculator stand out is its interactive, split-screen design. On the left-hand side, you're prompted to enter the necessary information to perform integral calculation. On the right-hand side, there's a live x-y axis which immediately adjusts your graph with the data you've inputted. Plus, it shows you the steps the solve the equation.

This interactive design is also available for other, even more complex online calculators including the Simpson Rule of Numerical Integration as well as a comparison of the trapezoidal rule and Simpson Rule which allows you to toggle back and forth between the two.

NA-Labs is another barebones site which offers five online calculators: the trapezoidal rule, Simpson's Rule, Riemann Right Endpoint Rule, Riemann Left Endpoint Rule, and Riemann Midpoint Rule.

Once again, you'll enter the function, upper and lower limits, and the number of trapezoids to use. The default results are displayed in degrees mode. You are given the option, however, to easily convert to radians for evaluating trigonometric functions.

WanerMath is another stripped-down site which nonetheless provides a number of useful resources for finite mathematics and applied calculus for students. These include online tutorials, review exercises, and true-false quizzes. In addition, the site is available in Spanish.

Instead of offering an online calculator like the options above, the trapezoidal rule webpage provides the step-by-step code to program your TI-83 graphing calculator to do this for you. After all, a webpage is handy enough, but being able to perform multiple trapezoidal rule calculations without needing Internet access is a big plus. You can also immediately use the data you generate for other equations and operations on your calculator.

The coding is relatively simple as there are only 20 lines required to compute left- and right-hand Riemann sums using the trapezoidal rule. While you're there, you can also grab the code to use Simpson's Rule, a 17-line program. You can't beat it: A few lines of code to perform heavy-duty calculations any time you have the need.

One of the oldest, unofficial Texas Instruments support sites, ticalc.org is loaded with useful information. Registered users can upload and download files, read and submit reviews, and rate files based on their quality. You'll also be able to access new games for TI calculators as well as patches and other fixes.

This site is useful because you may not want to manually key in the code on your TI-83 or TI-84 Plus. On ticalc.org's TI-83/84 Plus Basic Math Programs (Calculus) page, you can access almost 300 program files to download to your TI graphing calculator. This includes over 25 different trapezoidal rule calculator programs. In addition to the trapezoidal rule, many of these files contain multiple calculus-related programs you'll find handy too.

There is also a handy legend which indicates which features a file has: file with screenshots, file with animated screenshots, and file with reviews.

Then again, perhaps you want the software for a trapezoidal rule calculator to run on a machine other than a TI calculator. In that case, CodingAlpha is a site you should look at as it provides the code to do this in the C programming language.

In less than 30 lines of C programming code, you'll be able to calculate the trapezoidal rule on your own computer. Not only is the code provided, but there are handy troubleshooting tips too. The code utilized a GNU GGC compiler on a Linux Ubuntu operating system, but it should run on any other operating system too.

Users can also download C programs for other numerical calculations such as Weddle’s Rule Algorithm, Picard’s Method, and Euler’s Method.

Just like engineers don't use slide rules anymore, there's no need to calculate trapezoidal rule integrals by hand. Whether you want to use an online calculator or download code to your own graphing calculator or computer, there are many options available to let you work smart, not hard. That way, you can spend more time on the big picture issues of the problem you are working to solve.

*Need to calculate arc length? Check out **our how-to guide** to perform this important equation! *

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]]>The post SAT Calculator Hacks: Trigonometric Values, Graphing, And More appeared first on .

]]>The SATs (Scholastic Aptitude Tests) are among the more nerve-wracking of high-school experiences, as many colleges use the SATs as a primary factor when determining student admission. Scholarships and more can rest in the balance of an SAT score, leading to crippling test anxiety among even the most dedicated students.

Compounding matters is the fact that the test is timed, which can further increase a student’s anxiety. Even if a student is very well-prepared, knowing that a proctor is sitting with a running stopwatch can place an additional strain on a student’s psyche.

But this article isn’t meant to further stress out an already-anxious student. Once a student is comfortable with a calculator, many of the math problems on the SAT become routine. Read on to learn the very best SAT Calculator Hacks that we could find.

One of the biggest misconceptions regarding the SAT is the idea that the test can be taken without a calculator. While this is technically true, most students are doing themselves a great disservice by not obtaining a calculator and familiarizing themselves with the quick functions on it.

The Balance Small Business compiled a list of the 7 Best Graphing Calculators to Buy in 2018. Here is a rundown of some of the calculators from their list, along with corresponding links and price range for each:

As you can see, the price ranges for graphing calculators vary quite a bit. But all of these calculators are quite sophisticated, and more than capable of doing the job.

Parents and students should investigate the available options at the student’s school. Many schools have graphing calculators that they issue to students taking higher-level math courses, and some schools have a reserve of calculators from which they can lend. Students should take advantage of everything their respective schools have to offer, particularly as it concerns preparing for the SAT.

Once a student has decided on a calculator, becoming comfortable with the calculator is crucial. Even if a student does not purchase the newest or most-expensive calculator on the market, most of the current offerings are light-years ahead of what was available just five to ten years ago. Comfort, not the willingness to spend, is key when making a decision on an SAT Calculator.

Once a student has decided on a Calculator, the next step is learning the most effective hacks and shortcuts the machine has to offer. Read on to learn some of the best SAT Calculator Hacks.

Because the TI-84 and similar TI series calculators tend to be the most popular, they will be covered at length in this article.

The first series of calculator hacks apply to Texas Instruments TI-84 graphing calculators and will work on similar calculators within the TI series.

As noted above, these are considered the best calculators on the market by many people, and rightly so. TI graphing calculators can be found in high schools across the country, and TI models such as the TI-84 continue to rate very highly among professionals.

Before you dig into the TI-84 hacks, understand that there are two Math sections under the current SAT format. Under the current setup, students are allowed to use calculators (and the programs available on the calculator) for one of the two sections. It is highly recommended that students double-check all testing rules before the day of the test, as these rules are constantly influx and changing.

Here are some of the most helpful hacks for the Ti-84 Series:

This function converts decimals into fractions, if it’s mathematically-possible to do so. The FRAC Key can shave precious seconds by saving students the hassle of a long-form conversion. It also removes human error from the equation, assuming the student puts in the proper numbers.

Here is how to use the FRAC Key Function:

- 1Go to the MATH key on the TI-84 graphing calculator.
- 2After hitting the key, the first option will be the FRAC option. Click on this button.
- 3Hit the ENTER key, and the calculator will a decimal into a fraction.

Conversely, if the student needs to convert a fraction into a decimal, just hit the DEC key from the same menu.

This easy trick is potentially a major time-saver, allowing students to focus on the equations themselves and not stress over tedious conversions.

Programming your TI-84 calculator is the ultimate series of SAT Calculator Hacks. Below are some of the more frequently-used programs that you might want to consider programming into your calculator:

The quadratic equation is often used in trigonometry, and a student will absolutely be tested on their ability to implement the formula on the SAT. It’s very important for students to memorize the quadratic formula, as certain questions on the SAT’s No Calculator Math section will require its use.

The quadratic formula is **“Negative B plus or minus the square root of B squared minus 4AC all over 2A.”**

The formula is used to reveal the x-intercepts of a quadratic equation, also called the “**roots**” or “zeros” of the function (because the x-intercepts occur when y = 0).

So, when a student is seeking to find the x-intercepts of a quadratic on the Calculator Math section of the SAT, a quadratic formula program on your calculator could be invaluable.

The TI calculator website can show you how to install these programs for free. If the student needs help installing the programs onto their calculator, this video explains the process well.

Students can use programs to perform difficult operations, such as FOILing, factoring quadratics, solving quadratic equations using the quadratic formula, and solving systems of equations with two variables.

Solving Systems of Equations with Multiple Variables is a program that most students using a graphing calculator should pick up. This topic is very common on both the SAT and ACT.

In short, some systems have one solution, some have multiple solutions, and some have no solution. Students can use algebra to deduce these solutions, or they can utilize a program on their TI model calculator.

On the TI website, a search for “systems of equations” will generate numerous programs that complete the algebra automatically. This is another arrow in the quiver for a student taking the SAT.

A complete guide to the quadratic equation is available at the TI website referenced above, in addition to many more formulas and programs that students could find useful.

Another way to eliminate busy work is to program **Factoring** functions into your TI model calculator.

Factor form is a different way to represent an equation, and it can tell you the zeros of the function. Problems like this are peppered throughout the SAT.

It’s important for students to know how to Factor without using a calculator, as Factoring problems will appear on the No Calculator Math section of the current format SAT. However, programming Factoring functions into your calculator can again save some needless busy work, and help a student continue to cruise through the Math section.

Once programmed into a calculator, all a student needs to do is enter the A, B, and C values of a quadratic. The calculator does the rest, again saving precious time.

Here is how to use this program on your TI-84 or similar model calculator:

- 1Configure your equation into the form
*ax**2**+bx+c=0* - 2Enter these coefficients into A, B, and C values in your calculator
- 3Hit ENTER to get the solutions

Something to keep in mind is that Factor form is a bit different from solutions. If your solutions are 4 and -9, Factor form would be (x-4) (x+9).

**TO FIND A QUADRATIC EQUATION WITHIN WORD PROBLEMS – AND THEN TO APPLY WITHIN THE CONTEXT OF THE QUESTION – YOU CAN USE YOUR CALCULATOR TO QUICKLY FIND THE ZEROES WHILE YOU’RE FIGURING OUT A PART OF THE QUADRATIC.**

Additionally, if you see an x2 term in a word problem, use of a quadratic formula can help the student find and determine the zeros if not in a Factor or vertex form.

Two equations and two unknowns need to be solved for X and Y so that both of these equations are true.

Students will usually see them in some variation of this form:

**AX + BY = C**

**DX + EY = F**

ALGDOS is a multi-function program that includes a two-variable equation solver. Students can use this program to quickly find multiple variables when calculating a quadratic.

To use the program, the student will need to input the values of the coefficients. These values will be A, B, C, D, E, and F. After inputting the values, the calculator will then solve for X and Y.

This program is particularly useful for the word problems that are on the easier part of the test. These problems admittedly are not impossible to solve down, but having your calculator do it for you helps avoid careless errors.

Another very useful program is **Slope Intercept**, which will help students find the slope of a curve on their TI-84 calculator. Here is an overview of the concept.

The Slope Intercept program can take in two points and give you the slope and the intercept of a line.

This process can help a student with problems asking for the slope of the line, or problems asking which graph contains the points given by the test question.

To use the program, the student just needs to enter the points into the program and hit ENTER. The TI-84 will give the student the equation of the line, including the slope.

Graphing can be a bit time-consuming, but it can also be a life-saver if a student is stuck on a particular problem. On the SAT, an approximate graph can be close enough to the correct answer that the student does not need to solve the complete problem.

Students can use graphing to solve systems of equations, quadratics, or graphing problems. If the test presents a given equation and asks which of the graphs represents the equation, the student can then use the calculator to graph it.

Students can graph absolute values, inequalities, absolute value inequalities, parabolas, or ellipses. Graphing can find interception points that cannot be found with the linear equation solver, because some problems won’t be linear.

**MANY STUDENTS MAY NOT REALIZE THAT GRAPHING CALCULATORS STORE EACH AND EVERY TRIGONOMETRIC VALUE, INCLUDING ALL COSINES AND TANGENT. THIS CAN BE INCREDIBLY HELPFUL WHEN FIGURING OUT COMPLICATED TRIG PROBLEMS ON THE SAT.**

Common Trigonometric Values include angles of 0, 15, 30, 45, 60, and 90 degrees. Each of these can be stored in a TI series graphing calculator for quick reference while taking the test.

Students will also want to refer to this handy TI-84 Cheat Sheet, which condenses the latest TI-84 codes and functions into a single, easy-to-read document. This cheat sheet is specifically meant to be used with the TI-84 Plus, but many of the codes will work on other TI-84 series calculators.

Lastly, students may want to review this video on calculating Trigonometric Values. A better understanding of the principles at play will make for more effortless work when using a calculator during the actual SAT.

This article has covered the TI-84 and TI series calculators at length. While the TI calculators are deservedly popular, they aren’t the only calculators that students will potentially use on the SAT.

As mentioned at the top of the article, Casio makes two highly-rated calculators that deserve consideration: The Casio fx-9860GII, and the Casio fx-CG10 PRIZM.

While some of the Casio models do not have the same graphing functions as most of the TI models, Casio remains a viable alternative for students.

Ultimately, the decision on which calculator to use will come down to availability and a student’s comfort with a particular model, but it should be noted that many experts prefer Casio models due to their simplicity. In the case of a timed-test like the SAT, simplicity is elegance, as it potentially allows to complete problems more quickly and efficiently.

Programs and functions for the PRIZM series can be found at this link on Casio’s official site. Meanwhile, 9860GII users can click here for the complete user’s guide.

Students who are debating between Casio and TI model calculators can check out these links to help decide between the two:

Despite claims to the contrary, the SAT does not measure intelligence or accurately predict the type of grades a student will get in college. Rather, the SAT makes itself “harder” by quizzing students on obscure concepts within mathematics.

After all, complex mathematical formulas often take hours, days, or weeks to complete. The SAT is not measuring a student’s ability to complete these elite-level mathematical formulas, but instead testing students on things that most of their contemporaries probably don’t know.

In addition to the SAT Calculator Hacks presented above, it is recommended to SAT test-takers to brush up on the following Math formulas and topics:

Again, it can be extremely frustrating for a student who has prepared for months to come across a math question that they have no idea how to answer. It is important for parents and teachers to educate students on some of the realities of the SAT, which is that the test will ask a lot of obscure questions largely unrelated to practical situations, as well as present questions that students likely have not seen before.

Parents and teachers should want all students to do as well as possible on the SAT – after all, there’s room for everyone to succeed. Part of being successful on the SAT is understanding that the test will present some off-the-wall questions. Students can better prepare themselves by reading up on a few of these topics, and gain a working-if-not-perfect understanding of them.

The SAT is in many ways a sprint, as students hustle through questions in the interest of completing the test. A shot-in-the-dark guess is better than an unanswered question, so the testing format encourages students to not devote excessive time to any single question.

While students may not use their calculator on the bulk of the Math section, they can enter the test more confidently knowing that they can use a handful of stored programs to help complete it.

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]]>The post Where To Download Tangent Line Calculator For Free appeared first on .

]]>If you are newly enrolled in a higher-level mathematics course, the sheer number of variables (pardon the pun) can become overwhelming, particularly if you’re not a natural at math. But we are here to help with one of the more manageable problems in higher mathematics, which is where to find and download a Tangent Line Calculator for free.

While most smartphones come with simple calculators for quick arithmetic, more-complex equations seen in courses such as calculus will require sophisticated calculators. If you do not plan to invest in a handheld graphing calculator, or if you only need a Tangent Line calculator for limited use, there are a number of places on the internet where you can download calculators for free.

There was a time in the not-so-distant past in which graphing calculators were expensive niche tools. Today,

Fortunately for users, there are now a good number of sophisticated programmer and scientific calculators available online. If you want one you can download and keep, there are a number of apps and options for that as well.

A routine search on the internet will provide you with a number of options for downloading a Tangent Line calculator. We ran our own search, and here were some of the best options we found:

Apple users can download the Desmos Graphing Line Calculator on iTunes for free, making the mobile app a no-brainer for iPhone and iPad users. However, the app is only available for download for iOS users. The app rates 4.5 out of 5 stars, and per Desmos lets the user “plot functions, create tables, add sliders, animate your graphs, and more -- all for free.”

A very similar tool is available for free on the Desmos website. This is a viable alternative for desktop users looking for a free Tangent Line calculator. It operates almost identically to the Desmos iOS app.

GeoGebra offers a comparable tool. Their Tangent Line calculator is bare bones and straightforward, making it easy to use for those who are familiar with Tangent Line calculators. GeoGebra’s tool is not as educational as some of the other apps and sites.

Advanced and experienced users can take advantage of a free online scientific notation calculator at Web 2.0. This tool operates identically to a handheld graphing calculator. If you are familiar with graphing or scientific calculators but don’t want to invest in one, the tool at Web 2.0 offers a very viable alternative.

Another advanced option is available at OriginLab. This tool caters specifically to the scientific and engineering communities. OriginLab’s app “draws a tangent line at selected point of a data plot in a graph. A smoothing option is available for computing the derivative for noisy data.” The app is available for free download, with simple instruction available on the website. The website also offers a live chat in the event the user has any difficulty with the process.

If you are new to Tangent Line calculators, a slightly simpler tool is available at eMath Help. If you are not a natural at higher mathematics, the setup at eMath is more educational. Additionally, the tools available at eMath might assist you with better understanding the process.

BYJU's, “The Learning App”, offers tutorials, an online assistant, and very simplified format. You can directly access BYJU’s Tangent Line calculator here. The website offers a variety of sophisticated calculators in addition to Tangent Line. BYJU’s also offers an app, available for free download on both iTunes and Google Play.

Symbolab offers a number of tools including Tangent Line calculators for free on their website. Click here to access the Tangent Line calculator directly on your desktop or laptop. Mobile users can download the Symbolab Calculator app for free on iTunes or Google Play. Readers should note that the Symbolab app rates slightly lower than the Desmos app on both mobile platforms, but remains a very useful option for most users.

Finally, a breakdown and tutorial for calculating a tangent line is available at TutorVista.com. TutorVista offers 100% virtual tutoring, explaining that “the student works one-on-one with a professional tutor in a secure web environment using your existing computer, web browser and broadband Internet connection - no special equipment or software is needed.” While TutorVista charges a fee for some of their services, their Tangent Line calculator is available for free via the link listed above.

As you can see, there is no shortage of free and readily-available options for finding a Tangent Line calculator on the internet. If you are considering purchasing a graphing calculator, you may want to try a few of the options suggested above before buying one.

If you are brand new to the process of finding Tangent Lines, try not to become overwhelmed. There are numerous educational tools online that can help a new user learn how to calculate Tangent Lines, at which point you can take advantage of the free tools listed above.

To start, WikiHow explains “How to Find the Equation of a Tangent Line”. Per WikiHow, “unlike a straight line, a curve's slope constantly changes as you move along the graph. Calculus introduces students to the idea that each point on this graph could be described with a **slope**, or an instantaneous rate of change. **The**
**tangent line** is a straight line with that slope, passing through that exact point on the graph. To find the equation for the tangent, you'll need to know how to take the derivative of the original equation.”

MathCaptain takes the process a step further, explaining, “in Geometry, a straight line which touches a plane curve at a given point is called **the tangent line** to the curve or just tangent. Tangent line always just touches the surface of the curve at a point. The point at which it touches the curve is called **the point of tangency**.”

SoulMaths offers not only an in-depth explanation on Tangent Lines, but also a large number of quick links to related equations, tools, and theorems. The educational process on SoulMaths is very direct, but there is an almost-overwhelming number of links to related topics. While the site is very thorough, there is also the possibility that newer users could become lost. Still, SoulMath is a free, high-value site, and worth investigating.

As noted above, several of the sites that offer free graphing calculators also offer educational tools. TutorVista is likely the most comprehensive (due to the individual attention) but also likely the most expensive. BYJU’s and eMath offer a variety of educational tools and easy-to-understand explanations, most of which are available for free on their respective sites or apps.

Much like graphing calculators themselves, there is no shortage of educational tools and tutoring services available online. Most of them are available for free or at a minimum cost.

A practical way to apply Tangent Lines is on spreadsheets. Google Sheets can perform this function for you automatically. Follow this link to an instructional video on how to find slope and intercept in Google Sheets. Google Sheets is available for free in desktop and mobile app formats. The only requirement is that the user creates a Google account. Click here to go directly to the Google Sheets download page.

In a similar way, Microsoft Office users can create Tangent Lines with Microsoft Excel. The process is very comparable to using Google Sheets to create Tangent Lines, as explained above. Click here for complete directions on using Excel for this function.

Unlike Google Sheets, Microsoft Office and Excel are not free programs. However, you can try Office 365, Microsoft’s latest addition, for 30 days via this link. The regular prices for Office 365 Home & Student 2016 is $149.99 USD, while Office 365 Personal is $69.99. Both products rate four out of five stars. You can also find Office 2016 Professional for a fraction of the cost of Office 365, if you don’t need the latest features.

Lastly, if you want to learn more about running linear regressions in Google Sheets, this article from Wired covers everything you will need to know on the topic.

Today, we have more tools than ever before – both educational and practical – to help professionals and students easily work complex mathematical formulas. The days of being hunched over a cumbersome, expensive graphing calculator are behind (though that option remains if you’re feeling nostalgic).

There are no less than 10 or 12 locations online where you can access a Tangent Line calculator or use a spreadsheet to complete Tangent Line functions. Beyond that, there are a countless number of educational tools online that allow people to better understand complex functions such as Tangent Lines, allowing users to get the most out of the calculators.

For additional information on slope intercept or the best scientific calculator apps for Android and iOS, visit The Best Calculator. If you enjoyed this content, Like The Best Calculator on Facebook or Follow Us on Twitter.

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]]>The post How To Use Your Graphing Calculator As An X Intercept Calculator appeared first on .

]]>The advent of graphing calculators and scientific calculators has made advanced math much simpler to work with, but the best calculator in the world won’t do you much good unless you understand what you’re doing in the first place.

Any student, technician or engineer who’s working through higher math problems with a scientific calculator needs to have a firm grasp of the theory and principle behind the problems.

One area where these devices help hugely is in calculating quadratic equations and finding X intercepts.

Researchers and archaeologists have found quadratic equation-type problems that were being worked on as far back as 2000 B.C. Let’s go back to advanced algebra days. Algebra defines a quadratic equation as any equation with the form:

**ax2 + bx + c = 0**

In this type of equation, x represents the unknown, with a, b, and c representing known numbers (with a not equal to 0). If a = 0, then the equation is a linear equation rather than quadratic. The numbers a, b, and c are the equation’s coefficients; they can be defined, respectively, as the quadratic coefficient, linear coefficient and constant (or free term).

A quadratic equation that includes only one unknown is called “univariate,” and a quadratic equation that only contains powers of x as non-negative integers is known as a “polynomial equation.” If the greatest power is two, it’s a second-degree polynomial equation.

There are actually a few different approaches for resolving quadratic equations.

Quadratic equations are solved by factoring, by completing the square, using a quadratic formula or by graphing. Quadratic equations with either real or complex coefficients can have two solutions, called roots. These two solutions may or may not be real, and may or may not be distinct.

A quadratic equation of ax2 + bx + c = 0 can also be expressed as a product of (px + q)(rx + s) = 0. In a case like this, inspection can determine the values of p, q, r, and s in a way that shows the two forms as equivalent to each other. If the quadratic equation is expressed in that second form, then “Zero Factor Property” will show that the quadratic equation is resolved if px + 1 = 0 or rx + s = 0.

In most cases, factoring by inspection is a preferred method for resolving quadratic equations. In the case of x2 + bx + c = 0, the factorization would include the form (x + 1) (x + s), and the numbers represented by q and s would add up to b, with a final product of c.

Now that we have some ground rules on the theory behind quadratic equations, let’s talk a little about how to use a graphing calculator as an x intercept calculator. The great thing about these devices is that they feature built-in tools that enable you to work through these instances and find the intercepts without actually doing the algebra.

Remembering that a quadratic equation is one that can be expressed as ax2 + bx + c = 0, here’s how to use a calculator to work your way through this mainstay of algebra and advanced math.

Let’s think about definitions for a moment. We all know that the x-axis is the horizontal axis of a graph, and the y-axis is the vertical. An x-intercept, then, is the point on a line that crosses the x-axis of a graph and represents a function.

The x-intercept is expressed as (x,0) since the y-coordinate will always be zero at the x-intercept. So, if we already know the y-intercept of a function and the slope, the x-intercept can be calculated using the formula (y -b)/m = x, with m equal to slope, y equals zero and b equal to y-intercept.

In an equation that relates the first power of x to the first power of y, there will be a straight line on an x-y graph. To express that as a standard form, it would look like Ax + By + C = 0, or Ax + By = C. When this equation is rearranged with y by itself on the left side, it would look like y = mx + b.

This is the slope intercept form, with m being equal to the slope of the line and b being the value of y when x =0, making it the y-intercept. Rearranging an x intercept to standard form, then, isn’t much more than just simple arithmetic.

Using a graphing calculator to address a quadratic equation or simply as an x intercept calculator means having the ability to generate a graph of y =f(x) and the capacity to scale the graph for the size of the graphing surface. It also means being able to know that when f(x) = 0, x is the solution to the equation.

Graphing calculators may require the user to positioning a cursor at an approximate value for the root, and others might require brackets for the root on either side of the zero. The calculator then uses its algorithms to compute the proper position of the root, to the limits of its own accuracy.

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]]>The word “trigonometry” might strike a note of dread with many people as they recall struggling through high school math classes, but the truth is that trigonometry comes in handy in a wide range of science and math applications.

Having a calculator for advanced math and trigonometry work is great, but it can’t help you out unless you understand what you’re doing and know how to use it. We’re going to talk a little about how to use a tangent calculator with degrees and minutes, and some of the principles and theory behind these higher-math functions.

Think for a moment about a right-angled triangle. The tangent can be calculated using the lengths of the sides of this triangle – the adjacent side is horizontal next to the angle you’re wanting to analyze, and then the opposite side is vertical, opposite to the angle you’re analyzing. The hypotenuse of this triangle, then, is involved with the definitions of cos and sin, but not that of tan. So let’s think of it this way:

**Tan = opposite/adjacent**

In other words, opposite and adjacent correspond to the lengths of the sides that are given those names. If the hypotenuse is a slope, then, the tan of the angle of that slope also describes the rise of that slope (aka vertical change) divided by the length of that slope (aka horizontal change). With this in mind, the tan of the angle can also be described as:

**Tan = sin/cos**

When applied to the specific angle that you’re interested in, the tangent of the angle will tell you what the tan function returns. This is a function also known as “arctan” or tan-1 – it reverses the tan function, returning the original angle when it’s applied to the tan of the angle. For the sin and cos functions, arcsin and arccos serve the same purpose.

Tangents can be converted to degrees by applying the arctan function to the tan of the angle you’re analyzing. This equation describes how to convert tangents to degrees:

**Angle in degrees = arctan**

In other words, the arctan function can be thought of as the reverse of the tan function.

With a calculator (let’s go with the Texas Instruments TI-84 Plus for the sake of this discussion), it’s not hard to convert basic trigonometric functions and express them as angles, measured in degrees or radians. The TI-84 Plus in particular is capable of both directions, from angle to trigonometric measure and then back again. Here, we’ll use degrees instead of radians for consistency’s sake, but it’s no different from coming up with the same measurements in radians. All you need to do would be to set the calculator to the radians mode rather than degrees, as a first step.

Use the MODE key to set the calculator to Degrees mode, then press the Down arrow until you see the row with options “Degree” or “Radian”

Highlight “Degree” using the right arrow key, then press ENTER

Enter the inverse trigonometric function of the value you wish to see expressed as degrees

Press the 2ND key, then press they key for the trigonometric function in question

Example: to convert the sine of .5 into degrees, press 2ND followed by SIN. The display will then show sin^-1, or inverse sine. Follow that by entering .5 and closing parenthesis

Press ENTER and see the answer, expressed in degrees. Example: if sin^1 of .5 is entered, the calculator will give the answer of 30, which will be 30 degrees

Don’t forget the closing parenthesis

Remember that in trigonometry, the cotangent can be described as the reciprocal of the tangent. The formula for determining tangent involves dividing the opposite side by the adjacent side of the triangle. If the cotangent is the reciprocal, then, the formula that determines cotangent would involve dividing the adjacent side by the opposite side of the triangle. To put cotangent into a graphing calculator, the first step would be to know the angle (expressed in degrees) for which you’re trying to determine the cotangent.

Type 1 into the graphing calculator, followed by the division sign. The calculator will now be ready to perform a reciprocal calculation

Press the TAN button

Enter the angle for which you are determining the cotangent

Remember that arcsine can be expressed as the inverse of the sine function.

For example, if you were calculating the arcsine of 3, you would press 2ND followed by SIN, and sin^-1 would appear. Press 3 and the equation would display as sin^-1(3). From there, just press ENTER to calculate the answer.

Can you work your way through a system of linear equations by hand? Yes, but it’s a process that’s tedious, mistake-prone and time-consuming. Instead, let’s talk about how to solve linear equations or matrix equations with a calculator, referring back to our trusty TI-84 Plus graphing calculator.

This can be thought of as matrix A, multiplied by a vector of the unknowns and resolved with a vector B of constants. The calculator then inverts matrix A and multiplies A inverse and B to yield the unknowns in the equation.

A tangent line will only touch a curve at one point. A tangent line can be determined by using the point-slope method, aka slope-intercept. To put the slope-intercept equation in algebraic form, it would read y = mx + b, with “m” as the slope of the line and “b as the y-intercept, or the point where the tangent line meets the y-axis. To express this in algebraic form, this equation would be y -a0 = m(x – a1), with the slope of the line referred to as “m” and (a0, a1) as a point on the line.

If you’ve got a scientific calculator, it’s going to be invaluable for trigonometry and other higher math tasks. Once you’re familiar with how to use the calculator’s secondary functions such as SIN-1 and less-common functions (such as square root) and learn how to easily switch between degrees and radians, you’ll find these tasks are a lot easier and your calculator will serve as a true tangent calculator. Just remember to always include the close-parenthesis mark – leaving the right parenthesis off will likely return results that are far different from what you’ve been working toward.

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]]>If there’s one company that can take credit for developing the hand-held calculator, it’s Texas Instruments. They’re not just known for the calculator, though – TI was responsible for many innovations over the years, including the first silicon transistor (1954), the first transistor radio (1954), the first integrated circuit (1968) and even the first LPC speech synthesizer (1978).

Still, for years, TI was associated with calculators, starting with the popular SR-10 (1973) and SR-50 (1974) models. We’ve come a long way from the days of those heavy, clunky and expensive hand calculator – for higher math and scientific work, the TI-84 is now one of the go-to calculators on the market.

Released in 2004, the TI-84 Plus is a graphing calculator that superseded the TI-83 Plus model. As an enhanced version of the TI-83 Plus, the TI-84 Plus is similar in operation but does feature some improvements in hardware. The CPU is more than twice as fast, with a ROM archive that’s about three times as large. The TI-84 Plus’s USB port is USB On-The-Go compatible, a feature it shares with the next-generation TI-Nspire calculator.

Versions of the TI-84 Plus

**TI-84 Plus Silver Edition: **This upgrade to the TI-84 Plus was released in 2004 and features a 15 MHz Zilog Z80 processor with 24 kB user available RAM. It features a robust 128 kB chip (48 kB on newer models) and 1.5 MB f user-ready Flash ROM. Like the base model TI-84 Plus, the TI-84 Plus Silver Edition features a built-in USB port, built-in clock and assembly support.

** TI-84 Plus CE and TI-84 Plus CE-T:**Introduced in 2015, these two variants on the TI-84 Plus feature a rechargeable battery and 320x240 pixel color screen, with 154KB of user-accessible RAM and 3.0MB of archive memory. It uses Zilog’s eZ80 processor and is programmed in English, French, German, Portugese, Spanish and Swedish. This education market-oriented calculator comes in colors that include Classic Black, Silver Linings, Positively Pink, Radical Red, True Blue, Denim Blue, Plum Pi, Golden Ratio, Bright White and Lightning Blue.

The TI-84 series of calculators uses three different programs, easily programmed or downloaded into the calculator: TI-BASIC, Flash applications and Z80 assembly language (compatible with Flash). The exception is the TI-84+CE, with programs written in TI-BASIC, eZ80 assembly language or C programming language.

**TI-BASIC: **This proprietary software is similar to the BASIC programming language that’s been in use for PC machines for decades. It’s one of the most direct ways to program any TI calculator, but it’s slower than assembly language. It’s a better fit for performing repetitive calculation tasks or writing programs for solving math problems, rather than graphics-intensive applications or programming games. Its syntax is somewhat different from BASIC, with a character set that’s somewhat non-standard (such as all statements beginning with a colon, square and cube roots and other mathematical symbols).

**Assembly language: **Like with other machines, the TI-84 Plus’s assembly language is a low-level programming language with a strong relationship between assembly program statements and the machine code instructions of the architecture itself. In other words, an assembly language is more specific to the architecture of a particular computer, where high-level programming languages are portable across different architectures (but might require interpretation or compiling).

**C: **Developed in the early 70s, C is designed to re-implement the Unix system and has become one of the most prevalent programming languages of all time. It’s compatible with all types of computer architectures and can be found on everything from supercomputers to embedded microcontrollers.

USB On-The-Go is a technology that you’re probably familiar with but haven’t ever given much thought to. Introduced in 2001, USB On-The-Go allows tablets, smartphones and other USB devices to be compatible with digital cameras, mice, keyboards, flash drives and other devices. Its design allows the devices to switch back and forth and alternate between the roles of host and device – for instance, a mobile phone can operate as a host device when it’s reading from removable media but serves as a USB mass storage device when it’s connected o a host computer.

This is an especially handy feature when you want your TI-84 Plus and PC to talk to each other:

Run a cable from your calculator’s mini-USB port to the USB connector on your computer

Press o after connecting, which will allow the computer to recognize the action of turning the calculator on

You should see the TI Connect home screen, with a Select TI Device dialog box

Click on your device in the dialog box, then click the Select button

For many math functions, you’ll find yourself using the same number over and over, which makes it a good idea to store that number as a variable on your calculator. Here’s how:

Press [2nd] [MODE] to access the home screen

Enter the number you want to store as a variable, which can also be stored as an arithmetic expression. The calculator will evaluate that expression after you’ve taken all the steps for storing the number

Press [STO]

Press [ALPHA] and then press the key that corresponds to the letter of the variable that you’d like to assign to the number

Press [ENTER] to register and store the variable

**NOTE:** with graphing functions, polar equations, parametric equations and other operations, the calculator might change the value of the variable when the calculator is in graphing mode. For instance, if you were to store a number as variable X and then asked the calculator to determine the zero of the graphed function X2, the calculator will replace the number of that X variable with a 0, which would be the zero of X2. Be mindful of this for certain operations.

After the number has been stored as a variable, it can then be used in an arithmetic expression. Just place the cursor where you want the number to be assigned in the math problem, press [ALPHA] and press the key that corresponds to the variable of the number you want to use.

**Viewing graph and table at the same time: **This is a pretty handy feature for many situations. Just press y= and type the equations. Next, press the *mode *key and you’ll see a row on the screen that says FULL HORIZONTAL GRAPH-TABLE. Use the arrow over to GRAPH-TABLE, then press *enter. *Next, press the *graph* key to see graph and table simultaneously. Press the *2**nd* key followed by the *graph *key to access all the values in the table. To exit from this view, press the *mode *key and select FULL.

**Using lists to investigate transformation graphing: **Press the *stat *key and select the first option. In the list L1 enter -2, -1, 0, 1, 2. Next, press the *y+* key. To get *L1*, press the *2**nd* key followed by the stat key. You’ll see *L1* as the first option. You can then change your equation in *Y1 *to explore.

** Storing window setting: **You’ll find instances where it’s really handy to store your favorite window setting so you can recall it whenever you need. Just press the

The ACT puts strict prohibitions on which calculators are permissible during tests. Any calculator with built-in algebra systems (which rules out the TI-89 and TI-Nspire), laptops, tablets, cell phone calculators, calculators with a QWERTY keyboard and other types are prohibited. Using one of these machines can actually get a student thrown out of the test. Test proctors will warn students about this at the beginning of the test and will collect any prohibited calculators – sometimes leaving students to work out all problems by hand.

The TI-83 and TI-84 Plus, however, both fall into the graphing calculator category that’s permissible for this test. Educators want to stress, however, that what calculator a student chooses to use isn’t what’s important – it’s the information that’s put into the calculator and how the student uses that information.

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]]>The world is full of change. In fact, some might say that’s all existence consists of.

Perhaps this is why humans are so concerned with change. It seems we can’t get the idea of it off of our mind. Everybody seems to want a bit of change. Yet, when we get change, we still seem to want more change, new change, or old change. Rarely do we not want change at all.

What’s fascinating about math is that it offers advanced tools to measure change. In particular, when change can be described using functions, math is really effective at analyzing these functions and the various properties they have. These properties yield important information concerning whatever system is being studied.

In this article, we discuss concavity calculators, an online tool that many students use to analyze how functions change over time. First, we offer a brief overview of a concavity calculator, emphasizing its benefits and drawbacks. Then, we offer some tips on how to use a concavity calculator, ending with our final thoughts on the future of concavity calculators.

A concavity calculator is any calculator that outputs information related to the concavity of a function when the function is inputted.

Inflection points are often sought on some functions. These are points on the curve where the concavity of the function changes. Functions can either be concave up or concave down at any point on the curve.

In another sense, inflection points represent where the second derivative of the function is 0. In other words, where the rate of change of the rate of change is 0. Inflection points don’t always exist, as some functions don’t experience any change in concavity.

The best way to access information related to the concavity of a function is to use an online graphing calculator like the ones offered by WolframAlpha or Symbolab. These online calculators allow you to input a function in standard form, providing many different kinds of data concerning this function.

These platforms allow you to customize what data is displayed for each function. If you want to determine the inflection points of a function, then you just simply write “inflection points” before typing in the function.

Depending on which online concavity calculator you use, you will get vastly different results.

Some will only offer you the coordinates for the inflection points, not even offering a graph. Others will offer the inflection points, a graph, and some basic analysis. The best concavity calculators will offer all this with step-by-step guides as to how each value was calculated. Also, the best concavity calculators often offer practice problems and connections to real-world applications.

Most online concavity calculators are free. While you can purchase online concavity calculators, these are usually just gimmicks. Free versions are almost always available with comparable functionality. The only exception would be a concavity calculator that offered high-resolution graphs that other free applications simply didn’t offer.

Concavity calculators that are housed in the hardware of a more general graphing calculator, however, cost money.

The TI-84 Plus, for example, costs $108.00. It allows you to graph functions and analyze important points on the curve. However, in order to find the inflection points and determine where the concavity changes, some knowledge of basic calculus is needed.

The main benefit of a concavity calculator is that it makes finding some inflection points easier.

Students are first taught how to find inflection points in a first-semester Calculus course. Students are taught to calculate the second derivative and set it equal to zero in order to determine the x-coordinate of the inflection point.

Sometimes students are introduced to the concept of concavity and inflection points in earlier courses, though almost always on a cruder level. Calculus teaches you how to determine these points using derivatives, showing what these points say about the rate of change of the function.

Texas Instruments Ti-84 plus Graphing calculator - Black

- Real and complex numbers calculated to 14-digit accuracy and displayed with 10 digits plus a 2-digit exponent. Graphs...
- Sequence graphing mode shows time series plot, cobweb/stair-step plot, and phase plots. User-defined list names. Lists...
- Interactive analysis of function values, roots, maximums, minimums, integrals, and derivatives. 7 different graph...

However, calculating the second derivative can be a tedious process depending on the function. For some functions, calculating the second derivative might be almost impossible or practically unfeasible. This is especially the case for more advanced students who are often studying complicated functions. In these cases, a concavity calculator that can quickly calculate the inflection points is ideal, as this allows the student to avoid taking the derivative by hand.

Many graduate students also have to compute large amounts of data for some research they are engaging in. Instead of calculating the inflection points over and over again, these students can use the concavity calculate to expedite the process. This makes their work more productive.

In addition, a concavity calculator also allows students to be more creative with their work. If you’re able to analyze almost any function, then you don’t have to worry about picking a function that easily yields inflection points. Instead, you can study a funkier function with some unique properties, relying on the calculator to compute the approximate coordinates and show you an accurate graph.

The main drawback of a concavity calculator is that it encourages you to avoid exploring functions by hand.

Yet, this can be a beneficial activity from time to time, especially if you are pursuing a career in math. You will likely need to be able to graph functions and calculate first and second derivatives in the future. Many students anticipate this and ensure that they graph some basic functions by hand from time to time and analyze their properties.

By relying on a concavity calculator constantly, you can lose touch with these basic skills, which could impact your performance in later math classes.

Even further, understanding what an inflection point represents on a more practical level will be useful if you’re pursuing a highly mathematical career. If you use a concavity calculator every time you need to analyze the concavity of a graph, then you might lose touch with what computations you are even performing. This could be costly in a more practical career in which interpreting abstract information in relevant ways is the basis for your work.** **

The most important tip for using a concavity calculator is to set strict limits when it comes to using other websites. You want to concentrate your focus on the calculator only, as this will allow you to connect with the functions you are exploring on a deeper level.

Many students approach the use of online calculators with amazement, surprised that they are able to use the internet for school purposes. It’s not long before these students are distracted by some social media post or trending article.

The best way to prevent this from happening is to set clear intentions before you begin. Make it known that you intend to use the internet for school purposes only.

Some students find it effective to make simple compromises when negotiating with themselves. This can be as easy as promising yourself more personal computer time later after you’ve finished your schoolwork.

Some students try rewarding 30 minutes of schoolwork with 10 minutes of free internet time. We don’t recommend this approach, as we think the internet is a rabbit hole. Even if you’re able to follow your initial parameters, it’s likely that your attention will still be divided between the concavity calculator and your anticipated internet usage. This affects your level of concentration and productivity, preventing you from maker deeper connections with the information you are studying.** **

We think the future of concavity calculators entails integration with virtual reality headsets. We think these headsets will usher in a new era of education that is personal yet social and expansive at the same time.

We envision future students as no longer observing graphs of various functions from afar but instead sliding down their curves, climbing up their mountains, and probing their inflection points like a scientist taking data. This interactive form of education will provide our memories with richer material, allowing our recall to be sharper and quicker.

We think as technology evolves even further, computers will be integrated into human brains in order to boost our cognitive performance. This might make us smarter than any concavity calculator, though it’s not clear if we would be considered separate from a calculator or the same as one. Once we start inserting chips into our bodies, we’ve arguably fulfilled the prophecy of man becoming machine.

Some futurists think our brains are already the most advanced calculators in the universe. These visionaries think that rather than looking for guidance from outside of ourselves in the form of products or devices, we should be looking within. According to this theory, we are just as powerful as any machine we’ve created or can create. The key is to unlock this potential.

There are many ideas concerning how to unlock this potential. Ascetic study of math is certainly one way to unlock the deep abstract intelligence inherent within us all. Some gurus, however, teach meditation and yoga as another method of unlocking our potential.

All of this is to say that, while concavity calculators are important tools in the pursuit of knowledge, it should never replace our personal quest to manifest our innate intelligence.

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]]>The internet is an incredible tool for helping math students develop.

Online calculators, in particular, are often relied on by students because they allow such specialization. Students can use all kinds of online calculators that are specifically designed around a certain theme, like complex numbers, derivatives, or parabolas. This means that regardless of your math needs, there is likely an online calculator that will help you.

Online calculators are also free, which makes them ideal for anyone who cannot afford a more expensive graphing calculator.

In this article, we discuss vertex calculators, which can be found online or in many graphing calculators. First, we give a brief overview of vertex calculators, emphasizing their benefits and drawbacks. Then, we offer some advice on how to use them. Finally, we offer our thoughts on the future of vertex calculators.

Vertex calculators provide information concerning the vertex of a parabola.

Many graphing calculators, like the TI-84 Plus, allow users to graph parabolic functions by inputting an equation into the calculator. Users can then find the vertex of this parabola by using the “min” or “max” function on the calculator. Although this might be a more indirect route, it’s still effective.

- Real and complex numbers calculated to 14-digit accuracy and displayed with 10 digits plus a 2-digit exponent. Graphs...
- Sequence graphing mode shows time series plot, cobweb/stair-step plot, and phase plots. User-defined list names. Lists...
- Interactive analysis of function values, roots, maximums, minimums, integrals, and derivatives. 7 different graph...

Some advanced graphing calculators will come with more specific vertex calculators installed. Alternatively, some calculators will allow you to install third-party applications. In this case, if you buy these calculators, you might be able to download a customized vertex calculator for free.

Many of these will not only graph a parabolic equation and give you the vertex but also analyze other information like its domain, range, x-intercept, y-intercept, focus, and directrix. These are all important topics that anyone studying a parabola will be interested in.

Online calculators have the same functionality as graphing calculators while also providing a more seamless user interface. Some of the most popular vertex calculators online include Symbolab and Math Captain.

Online vertex calculators are categorized either as advanced vertex calculators or basic ones.

Basic ones, like Math Captain, offer a short discussion of quadratic functions and parabolas before providing users with three input possibilities. These correspond to the variables a, b, and c that are used in the standard form of a quadratic function. You can input various values here to influence the parabola that the calculator analyzes. After entering in three values, the vertex calculator will give you the coordinates of the vertex.

Advanced vertex calculators, like Symbolab, allow you to include more than just numbers in the input box. These calculators allow you to write what information you want like “directrix” before you type the function. Additionally, these calculators offer a more fluid interface that maximizes the functionality of your keyboard. You can often enter all kinds of unusual and funky functions in these calculators and get a thorough analysis.** **

What’s great about many of these online advanced vertex calculators is that they also generate practice problems based on the input of a function. This is a critical tool for beginner math students who are starting to study parabolas.

Many students use online vertex calculators to help with their homework but end up using them above and beyond what is required. Many students are looking to test their knowledge in ways other than those recommended by their teacher. This doesn’t mean abandoning your homework, but also exploring other questions related to a specific function.

In this sense, the best online vertex calculators will inspire students to deepen their learning in other areas. Some vertex calculators offer practical questions involving common parabolas studied in physics. These questions can be very grounding for students that are overwhelmed by the abstract nature of math.

Furthermore, online vertex calculators can be accessed anywhere where there is internet and a device that can connect to the internet. This levels the playing field when it comes to math education, meaning that students all over the world have access to the same tools.

Furthermore, this means that students can potentially use vertex calculators on their smartphone. This would be ideal if you were trying to do homework on the go.

The main drawback of a vertex calculator is that they offer the opportunity for abuse.

Graphing parabolic functions by hand and determining vertex coordinates by hand is a great way to sharpen your math skills. This is especially important if you plan on pursuing a career in math, as you won’t want to lose these basic skills. If you rely on a vertex calculator every time you need some piece of information related to a parabola, then you might gradually lose this knowledge.

This could also be detrimental come test time, especially if graphing calculators are not allowed.

Additionally, there is an overwhelming number of vertex calculators offered online, each with its own unique interface and features. This can be frustrating, as it can take a while to find one that meets your preferences.

In this sense, sometimes technology can actually interfere with our education. Some students spend more time searching for the best vertex calculator than actually using one. Additionally, some students use online calculators as an excuse to browse the internet and procrastinate. These students might be better off just giving up math and exploring a field they are more naturally interested in, like technology, computer programming, or marketing.

Thus, since vertex calculators offer a shortcut for math students, they can sometimes obscure where our real interests lie. Some of the most uninspired math students are able to pass their courses for many years using online calculators. They can’t rely on these tools forever, and eventually, they must do the dirty work of mastering the underlying concepts or admitting their disinterest.** **

This leads to our next tip, namely that you should control how you use a vertex calculator.

We recommend blocking websites that often distract you and setting strict limits before using a vector calculator. Even though these tools can be very helpful, they are often within a click of the rest of the internet, which can be a rabbit hole for many.

Many users like to bookmark their favorite vector calculators so that they can click the link the moment they open their web browser. Other users like to download vertex calculator applications to their desktop so that internet connectivity is not even needed. This reduces temptations to use other programs, resulting in enhanced productivity.

Regardless of what technique you use, it’s important to stay balanced as you use a vector calculator. This means taking a break from it every now and then and analyzing a function by hand, plotting the graph and calculating the vertex using nothing but a pencil and some paper.

Another good tip is to share your favorite vertex calculators with your friends. Many of these tools are underused simply because students don’t know they exist. While they shouldn’t be relied on, they can certainly be helpful if you are starting to study parabolas.** **

We think vertex calculators in the future will be integrated with virtual reality headsets.

We think future students will be able to interact with parabolic functions on a more intimate level than ever before. Students will be able to not only observe a graph of a function but also climb it like a tree, exploring its curves, stroking its anomalies, and lying on its continuous form. This will allow students to multi-task in novel ways, exercising while also learning about parabolic equations.

In the farther future, we’re not sure that vertex calculators will be distinct from us. We think that our technology will eventually become so small that it will be implanted in our brain. Thus, we might only need to think about a function in order to get a view of its graph and determine its vertex.

Many people searching for a vertex calculator forget that they are already equipped with one of the most advanced vertex calculators on the planet. Every day, our brains help us navigate the spaces of our world which are inhabited by objects with parabolic properties. At best, calculators simulate the technology of the brain which is constantly working to interpret sensory information and compute outputs that support survival.

Calculators are merely concerned with fulfilling a task. Brains, however, must also ensure the continuation of the organism. This a tall order, so it’s no wonder that most of us are unable to harness the mathematical tools that lie deep within.

The boundaries that separate us from these internal calculators can be dissolved through a number of means, however, and studying math is one method.

While vertex calculators can support your studies, they should never replace them. Even if you don’t plan on pursuing a career in math, all of us could benefit from understanding parabolas without relying on a vertex calculator.

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]]>Math allows us to break up the world into little abstract pieces so that it’s easier to understand. By doing this, we can study specific parts of the world in isolation, uncovering their properties on both a microcosmic and macrocosmic level.

Calculators are one tool that many people use to enhance their study of math. Function calculators are especially helpful, as they allow you to input functions on the calculator and receive all kinds of output information.

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In this article, we discuss function calculators in more depth, giving a brief overview of them and emphasizing their benefits and drawbacks. Then, we give a step-by-step guide on how to use a function calculator, ending with our thoughts on the future of function calculators.

Function calculators are just a specific type of calculator that anyone interested in math can benefit from.

Most commonly, students use function calculators when they are learning about various functions, though professors also use them both to teach and to do research.

Some of the most advanced graphing calculators, like the TI-84 Plus CE, have color graphing applications that allow the user to enter in multiple functions and view the graphs of these.

Texas Instruments TI-84 Plus CE Graphing Calculator, Black

- High-resolution, full-color backlit display
- Sleek design
- Rechargeable battery

Some graphing calculators will set limits on how many functions you can graph as well how many variables are allowed in the graphed function and what information is displayed on the graph. The most advanced graphing calculators will even allow you to graph functions of 3 variables or more. These are usually found online, like the one offered by GeoGebra.

Thus, in one sense, function calculators are really the same thing as graphing calculators. Function calculators just emphasize the analysis of functions and provide information that students usually seek from functions. This includes determining x and y-intercepts, max and min values, the domain and range, vertex values, and many other outputs.

The most effective function calculators will allow you to customize what information is displayed once you input a function. The most basic function calculators, on the other hand, will only allow you to input the simplest of graphs, usually with no more than two variables.

Two of the most popular online function calculators are offered by Symbolab and Desmos. Most online function calculators will also offer you other tools to enhance your math education, so make sure you have the function calculator option selected before you begin your work.

Function calculators usually work by allowing users to enter a function to analyze. Some function calculators allow users to enter in output information first in order to determine what function(s) would yield this information. Regardless, function calculators are designed to shine a spotlight on some function you’ve been considering.

Functions are important in disciplines other than math, most specifically physics and engineering. They are condensed containers of information. Like a human being, each function is totally unique yet shares qualities with other functions.

Modern math students are constantly standing on the shoulders of giants, relying on the knowledge uncovered by past mathematicians in order to push the subject forward. The explorations of many famous mathematicians have led to many modern theories and shortcuts that allow us to compute values faster than ever before. Thus, function calculators allow us to expedite our learning and benefit from the discoveries of past titans in the field.

Without a function calculator, we would have to graph each function by hand as well as manually calculate important values. While this might be tolerable at first, eventually this practice would become impractical, especially as you moved on to the higher math classes. In some advanced classes, not only is a function calculator helpful, it’s actually a necessity.

What’s really great about modern function calculators is their ability to be accessed online. This truly levels the playing field when it comes to math education, allowing anyone with an internet connection to graph and analyze complex functions. Some function calculators will even allow you to download them so they can be used offline.

Some students who would usually not be inspired by math topics are surprised to find themselves not only enjoying the subject but considering a career in it. Function calculators are especially helpful for these students who want to explore a topic in more depth. Many beginner students are fascinated by how space and extension relate to abstraction, making function calculators which deliver sharp, colorful graphs an indispensable tool throughout their educational process.

Some of the most advanced function calculators will allow you to customize what information is displayed upon entering a function.

This is especially useful for more advanced students who are studying a certain function. This happens frequently in graduate school, as many students zero in on a segment of math that they are interested in, focusing on analyzing some shape or structure that can be described using the language of functions.

These students would benefit from a function calculator that can be modified to display information relevant to their research. Some graduate students need to compute large amounts of data concerning many types of similar functions. In order to avoid spending countless hours doing this by hand, these students elect to use an online function calculator that can be personalized. This makes their work more efficient.

The main drawback of function calculators is that they can lead to you relying on a calculator in order to remember the properties of a function.

Learning the properties of many functions is important if you want to continue studying math in the future. Many higher-level math classes will require you to know the properties of some functions in order to enroll. Graphing some of the most popular functions by hand and probing their properties can be a great way to keep your skills up to date.

Like a used car, your mathematical mind must be occasionally oiled and tuned up to facilitate optimal performance. Constantly using a function calculator is like procrastinating when it comes to taking the car in to get an oil change or check-up. You might be able to get by for a bit longer, but one day your laziness might come back to haunt you.

Using a function calculator can be very easy as long as you are able to recognize what information to enter and where to enter it. Most online function calculators will give an initial blank asking for you to type in a function. When you type in the function, make sure you copy it down verbatim, using any special characters or symbols that might be necessary.

More complicated functions might involve going to specialized websites. If a certain online calculator can’t analyze a function with a certain character, then try googling the function and seeing what search results you get.

After you’ve found an online website and correctly entered the function, hit “go” or “graph”. Some online function calculators will simply require you hit the return key. After you do this, a graph of your function should appear as well as any data that you requested.

Some function calculators will offer to show you the work required to calculate certain function values. Sometimes you have to select the “show” option in order to access this feature. This is especially helpful for students who are just being exposed to a function for the first time.

Lastly, many function calculators will allow you to store functions that you might want to use in the future. This can be helpful if you want to compare many functions but don’t want to re-enter each one every time. Many function calculators will have helpful features like this that can only be discovered by experimenting with them.

We think the future of function calculators will be truly radical.

We see function calculators as being valorized not only as tools in the future but also as legitimate teachers. We mean this on both a metaphorical and literal level. We see math students of the future using virtual reality headsets in order to engage with numbers and functions on a more personal level.

We can envision a future in which students graph a function and then are able to enter the world of the graph, climbing on curves like mountains and walking along lines like a trail. Why learn from a professor when you can learn from the numbers or functions directly?

In this sense, we see the future of function calculators as coinciding with the future of technology. As technology changes, so will the tools available for us to study math.

In fact, future technology could be so powerful that modern function calculators become obsolete. Perhaps future function calculators will not require the use of some external hardware but will instead be integrated into our neurochemistry, allowing our brains to transform into function calculators literally in the blink of an eye,

Whatever happens, we think it will be truly revolutionary.

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]]>The internet is a fabulous tool for anyone studying math, though it can also be overwhelming at the same time.

For any given topic in math, there is an infinite array of resources that the internet offers. However, sometimes it can be difficult to figure out which resource to utilize. This can impact your productivity, especially if you’re a student on a tight schedule.

In this article, we discuss parabola calculators, one popular resource online that many math students use. First, we give an overview of parabola calculators, emphasizing their benefits and drawbacks. Then, we offer some tips for anyone trying to choose a parabola calculator. Finally, we end with our thoughts on the future of parabola calculators.

First and foremost, a parabola is a plane-curve that appears U-shaped and is mirror-symmetrical. The parabola shape has many applications in physics, engineering, and the sciences, and is studied comprehensively in math.

A parabola calculator is any calculator that allows you to input information related to a parabola and receive various output information.

These are usually available online, though technically any calculator that gives information concerning a parabola could be considered a parabola calculator. Many advanced graphing calculators have applications related to parabolas, allowing them to transform into a parabola calculator while also retaining other functionality.

Online parabola calculators don’t necessarily have limited functionality. Some online parabola calculators are certainly simple while others are much more dynamic.

The most basic online parabola calculators will allow you to input a parabola equation in standard form and will offer you the x and y coordinates of the __vertex__, __focus__ and __directrix__. Some basic parabola calculators will also provide the parabola equation in vertex form.

More advanced parabola calculators provide this information while also providing a graph of the parabola. Among advanced parabola calculators, some offer simple graphs while others offer graphs with more enhanced graphics.

__Symbolab__ offers one of the more advanced online parabola calculators while __Omni Calculator__ offers a more basic version.** **

Parabola calculators expedite calculations related to parabolas, allowing us to study these shapes more efficiently. Parabola calculators can be especially useful for math students who are learning about parabolas for the first time. Many students like to use advanced parabola calculators to also study how certain equations look when graphed.

By comparing the graphs of various functions, students are able to understand how changing parts of an equation influences the graph of that equation. This visual understanding can be corroborated by information related to the parabola vertex, focus, and directrix.

Many students like to learn visually in this way, thus making advanced parabola calculators practically a necessity when first learning about parabolas. Many beginning math students comment that the subject is so abstract and can be difficult to ground in real-world applications.

Being able to visualize a graph of an equation can help students struggling with the abstract nature of math, making advanced parabola calculators invaluable. Basic parabola calculators can also be helpful for certain homework assignments when quickly determining parabolic values is desired.

For example, some students in more applied fields have to compute large amounts of data concerning differently sized parabolas. Many advanced parabola calculators would be inefficient at handling this task since they would graph the equation in addition to computing various values. This would slow down the online calculator, making your work less efficient.

A basic parabola calculator, however, would allow you to quickly change input values to determine crucial outputs. Some of the best parabola calculators will even allow you to select which values you’re interested in computing, making your job even easier.

The main drawback of a parabola calculator is the same drawback that plagues any other calculator. Relying on these devices can actually detract from learning, as our technology performs the computations that we could have performed by hand.

Not every parabolic computation can be performed by hand, of course. Certain complicated functions make determining coordinates and values difficult if not impossible. In these cases, an online parabola calculator is ideal.

Yet, in most situations, students are seeking a parabola calculator to help with a homework assignment or understanding some mathematical concept. Many of the equations that students deal with in these situations are conducive to performing calculations by hand.

However, many students get lazy over time and forget to sharpen their skills, leading to poor performance come test time. This is especially the case when the test requires that students show their work, as many students have forgotten the core concepts due to their reliance on an online calculator.

Without a parabola calculator, students would have to perform all their calculations manually, which would keep their skills fresh. Not being dependent on a parabola calculator is even more important if you plan on entering some career that deals with numbers.

In these cases, you want to keep the __“math” part of your brain__ active and strengthened so you can perform optimally at your job. Even if your job doesn’t entail work related to parabolas, it might still involve analytical work that uses a similar part of your brain.

In this section, we discuss 3 tips that readers can remember when choosing a parabola calculator online.

We recommend beginning your search by clearly setting your intentions. This will ground you before you enter the chaotic whirlpool that is the internet. Additionally, it will also force you to consider why you need an online calculator in the first place, which could help narrow your selection.

A good way to do this is to close your eyes, focus on your breathing, and repeat your intentions back to yourself. You can do this silently, out loud, or you can even write them down. Some people even draw their intentions.

Regardless, the point is to take several moments to consciously acknowledge what you are seeking and why you are seeking it.

Many students use a parabola calculator simply because their teacher said it was allowed. Before automatically following these instructions, you should reflect on how necessary a parabola calculator is. Some students abuse this permission in order to avoid mastering some math concept they are shaky on. Alternatively, some students simply want an excuse to access the rabbit hole of the internet.

Whatever the case may be, make sure your intentions are genuine.

If you’ve determined that using a parabola calculator is ideal, then we recommend using a more advanced parabola calculator. These tools offer you the ability to graph your equation, allowing you to supplement your computations with a visual aid.

Many beginner math students avoid advanced parabola calculators in favor of basic calculators that are quicker. Yet, even though they finish their homework faster, these students often perform poorly on the relevant test.

This is because the test requires them to describe the visual nature of each parabolic function they encounter. Since they never deepened their understanding of this component of parabolas, these students inevitably suffer.

There are many parabola calculators to choose from online. Finding the one that you like the best can be difficult, especially when looking up “parabola calculator” seems so many different results.

When you do find a parabola calculator the meets your preferences, make sure you bookmark it. This will make it only a click away the next time you need it. Also, it will prevent you from having to scroll through endless search results simply because you forgot the URL.** **

We think parabola calculators are indispensable tools for modern students. This applies not only to math students but to students in other disciplines. Parabolic shapes are prevalent in many fields, making their study practical in addition to abstract.

We think advanced parabola calculators will help neutralize the abstract nature of studying parabolas. This is because they allow you to see a graph of the parabola you are considering. Sometimes, they even allow you to compare multiple graphs and compute additional values.

We think that online parabola calculators will evolve as computers evolve in the future. We can imagine a future in which math students use virtual reality headsets in order to access a parabola calculator.

The parabolic application on these headsets would offer a fully immersive experience, allowing users to not only graph parabolic equations but climb them. Future students will be able to use parabola calculators to interact with mathematical avatars, allowing for a more personal kind of learning. Why learn from a teacher when you can learn from a number or equation directly?

While this might seem unrealistic now, we think this future is just around the corner. It’s heavily contingent upon the development of virtual reality headsets, which would change the educational landscape significantly.

We imagine the future of education as entailing an embrace of these cutting-edge technologies, making the learning process more intimate and life-sized than ever before.

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