# Solving Equations by Graphing on a Graphing Calculator

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• 0:01 What Do We Mean By Solving?
• 0:55 Zero Value
• 1:52 Maximums & Minimums
• 2:41 Intersections
• 3:21 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

One of the most useful aspects of having a graphing calculator is to be able to use it to solve equations. However, the word 'solve' has multiple potential meanings, as this lesson will demonstrate.

## What Do We Mean By Solving?

In this lesson, we're going to take a look at solving equations by graphing them on a calculator. However, before we begin, I think it might be useful to think of what we mean by the word solving. The word can really have different meanings depending on what it is we want to do. If you're just looking to figure out what x is when y is equal to zero, we can do that. However, using a calculator to solve equations alone would really limit our potential here. We can also use calculators to find maximums and minimums, both of which are of great importance when you start to study precalculus and beyond. However, more than that, we can also find where two functions meet, letting us find an answer that works for both of them. As you can see, there's quite a bit that can be meant by that one word 'solving.' In this lesson, we're going to learn how to do all of those things with a graphing calculator.

## Zero Value

When many people think of solving an equation, they are most likely thinking back to days in algebra class, where they were asked to solve a single variable equation. A single variable equation is an equation with only one unknown, most often x. Luckily, graphing calculators make quick work of those problems. Let's say that you were asked to find value of x in the equation 2x = 30 - x. Now, you can't just plug that into the graphing function of your calculator. Instead, you should get everything on one side. That means that you're really looking for 30 - 3x since if you subtract 2x from both sides, that's what you'll get. Now plug that equation into your calculator. The graph comes up, and the line it produces meets the x axis at 10. That is our zero value, or the answer to what x is when y is zero. If you want, you can plug 10 into the above formula and see that it indeed is the value that we were looking for. However, let's say you are looking for a range of something. Say that you wanted to know the absolute lowest or the absolute highest that a function can achieve. After all, a simple linear function will eventually find every value of x and y, but a parabola, or a graphed function of x^2, definitely won't.

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