Question

Find vertex of:

y=(x-4)(x+8)

Answer 1

(-2,-36)

Explanation:

`y=(x-4)(x+8)`

1) Find the zeros of the parabola

The zero-product property states that any value, when multiplied by 0 will equal 0. Therefore, to make y=0, either (x-4)=0 OR (x+8)=0.

Therefore, x=4 and x=-8.

2) Find the x-coordinate of the vertex

To do this, we take the average of our zeros.

`(4+(-8))/(2) \\=(-4)/(2) \\=-2`

Therefore, the x-coordinate of the vertex is -2.

3) Find the y-coordinate of the vertex

Plug the x-coordinate back into the original equation

`y=(-2-4)(-2+8)\\y=(-6)(6)\\y=-36`

Therefore, the y-coordinate of the vertex is -36.

Therefore, the vertex of the parabola is (-2,-36).

I hope this helps!