Question

How do you solve `x^2-2x-8=0` graphically?

Answer 1

`x = -2 " or "x = 4`

Explanation:

First you need to have a graph to be able to use it.

It will be a parabola which you can obtain by plotting points.
The equation of the graph of the parabola is

`y = x^2 -2x-8`

Now compare the equation we are asked to solve with the equation of the parabola...
`x^2 -2x-8 = color(red)(y)`
`x^2 -2x-8 = color(red)(0)`

We can see that `color(red)(y)` has been replaced by `color(red)(0)`

`y = 0` is the equation of the x-axis.

In other words the question is asking all of the following questions - different ways of asking the same thing.

"Where does the parabola cross the x-axis?"
"What are the x-intercepts?"
"What are the roots of the equation"
"Solve the equation" `x^2 -2x+8 = 0`

Read the two values off the graph to solve the equation.
`x = -2 " or "x = 4`

graph{x^2-2x-8 [-6.82, 13.18, -9.16, 0.84]}