Question

How would I graph something like x^2 = 16?

I don't understand how it would be possible to graph that. It looks like only plus or minus four works in that situation, but how would you graph more than 3 points? (X intercepts, vertex). How would you find that vertex?

Answer 1

First of all, you are right, the `x`-intercepts are `(-4, 0)` and `(4, 0)`. But we need to find the vertex. With three points, we can draw a pretty accurate graph

How to find the vertex:

The vertex is at the halfway point of the zeros. So for the `x`-coordinate, we need to find the halfway point between `-4` and `4`, which is `0`.

For the `y`-coordinate, we use this `x` value, `0`, and solve for `y`:

`0^2 -16 = y`

`-16 = y`

So the `y` component is `-16`

So we have three points: `(-4,0)`, `(0, - 16)`, and `(4,0)`

Let's see how this looks graphed:

graph{y = x^2-16}