Question

How do you solve `2x^2 = 3x^2 -2x-8` by graphing?

Answer 1

`x=-2,x=4`

Explanation:

First, you need to solve for 0 on one side. This can be done by subtracting `2x^2` from both sides.

`x^2-2x-8=0`

Now we solve for 0 because when we plug this equation into a graphing calculator, we need to know what we're looking for. So solving for 0, we're looking for where the equation `x^2-2x-8` is equal to 0.

Now in order to plug this equation in, you need a graphing calculator or your computer (if you're on your computer I recommend a nifty website called desmos.com, it's very interactive which helps).

graph{x^2-2x-8 [-18.02, 18.02, -10, 9.01]}

Here is what the graph will look like, now in order to find the points where the graph is at `y=0`, we will need to either drag our mouse on the graph to interact with it if you're on a computer, or find the zeroes using a function on your calculator. If you're on a TI-83/84, the steps will be to graph, hit the second button then hit trace (calc) then go to the second option on the menu shown.

Now interacting on the graph, we can find that the zeroes are -2 and 4.