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## Get ready for AP® Calculus

### Course: Get ready for AP® Calculus>Unit 7

Lesson 6: Solving equations by graphing

# Solving equations by graphing: graphing calculator

We can approximate the solutions to any equation by graphing both sides of the equation and looking for intersection points. If we have a graphing calculator, we can get a very good approximation of the solution.

## Want to join the conversation?

• Wouldn't the graph of -ln(2x)=2|x-4|-7 be a line with only one solution for x regardless of the y?
• Much like Sal did in the video, the graph has two functions, y=-ln(2x) and y=2|x-4|-7. If plotted on a graphing calculator, there are two intersections and solutions for x: 0.5 and 6.238.

Though I am unsure why the graph of -ln(2x)=2|x-4|-7 is a line, the line is approximately x=6.238, which is the other solution.
• is it possible to solve it by not using the calculator? Is it allowed to use calculator for tests?
• I suppose you could algebraically solve this particular problem by setting the functions equal to each other although this would probably be a harder process and you would still need to do calculations with e, which would probably require a calculator of some kind, if not a graphing one.
If having a physical calculator is the problem, there are programs you can use such as websites and apps that accomplish the same thing.
As for being allowed on tests, that is something to ask your teacher and they might even have a class set. For standardized tests like the SAT, there is a list of acceptable calculators (they won't let you use an app on your phone for obvious reasons) and while it is possible with a 4-function or scientific calculator, graphing is recommended. If the need be you could always borrow one from a friend or fellow student if it is just for one test (I did this myself when I took the SAT and borrowed a scientific calculator, but I was already familiar with it. Using a calculator for the first time on an important test could present a problem). Other tests might be possible without calculators in general, but become easier (and quicker) with them.
• how would you graph that graph?
• Use a graphing calculator! Sal is using desmos.com
• Why are intersections of two different graphs called 'solutions' and not 'intersections'?
(1 vote)
• We call the point of intersection a solution as it is a point which satisfies both lines. So, it is a solution to the "system of lines".

Calling it the intersection isn't wrong per se. But, an intersection doesn't have an algebraic meaning. It can only be interpreted visually. So, we use the term "solutions" instead.
• how do you solve the practice exercises if you dont have a Desmos graphing calculator
for example:-ln(2x)=2|x-4|-7
(1 vote)
• You can also go online and search up Desmos Graphing Calc =)
(1 vote)
• How does setting both sides of the equation equal to y a way to solve it and finding the intersections as solutions? I'm very confused on how this actually works.
(1 vote)
• I use desmos.com
(1 vote)
• Iam having trouble , iam not Abel to enter answers , like iam , solving equations when I have to put answer in square or cube , I can’t , like is that specific key I have to press on keyboard ⌨️ , and can I use calculator to solve the equations ,
Sumaiya Ferheen
Thanks
(1 vote)
• For some questions there won't be a "Show Calculator" button there, but if there is one, just click on the button. Answering your question about keyboard inputs, you could use the "^" key which you can access by pressing shift and 6 at the same time, and then enter in whatever number you want. But there is also another method. Which is just clicking the answer box and then selecting the small icon "e^x."

Keyboard Input Example
y = x^2 + 3 or y= x^3 + 3

(Note: You can also do this on your graphing calculator the same way, as the "^" symbol is also on there)