Question

How do you solve `x^2 - 16 = 0` graphically?

Answer 1

On the graph below the x-intercepts are found at `x=-4 and x=+4`

Explanation:

You need to draw the graph of `y-x^2-16` first.

This can be done by plotting points which you work out using the equation.
Choose several x-values... negative, zero and positive, then calculate the corresponding y-values.

The graph is a parabola - draw a smooth, free-hand curve through all the points.

Now you can solve the equation graphically.

Compare the equation of the GRAPH with the EQUATION to be solved.

`x^2 -16 = color(red)(y) and x^2-16 = color(red)(0)` This gives `color(red)(y=0)`

`color(red)(y=0)` is the equation of the `color(red)(x)`- axis.

The question is actually asking..

"Where does the parabola cross the x-axis?"

OR:

"What are the points of intersection of the two graphs
`y=x^2-16 and y=0`?"

On the graph below the x-intercepts are found at `x=-4 and x=+4`

(Note that the y-intercept is at `y=-16`)
graph{y=x^2-16 [-9.79, 10.21, -5.88, 4.12]}