USING A VERTEX CALCULATOR FOR PARABOLA
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.
AN OVERVIEW OF A VERTEX CALCULATOR
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 10...
- 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 styles...
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.
THE BENEFITS OF A VERTEX CALCULATOR
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 DRAWBACKS OF A VERTEX CALCULATOR
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.
TIPS FOR HOW TO USE A VERTEX CALCULATOR
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.
OUR FINAL THOUGHTS ON THE FUTURE OF VERTEX CALCULATORS
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.