Question

How do you solve `x^2-x-4=0` graphically?

Answer 1

From the graph we get `x~~ -1.6 and x ~~2.6`
We cannot find the exact answer graphically.

Explanation:

First you need to draw the graph of the parabola as
`y = x^2 -x -4`

You can do this by plotting points.
Draw up a table, choose some x-values and work out the y-values.

If you compare `color(red)(y) = x^2 -x -4` and `x^2 -x -4 = color(red)(0)`, you will see that the only difference is that `y=0`

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

"Where does the parabola intersect the x-axis?"
OR
What are the x-intercepts for this graph?"
OR
Find the roots of the equation `0 = x^2 -x -4`

From the graph we get `x~~ -1.6 and x ~~2.6`
We cannot find the exact answer graphically.

graph{x^2-x-4 [-2.365, 2.635, -1.62, 0.88]}