Question

What is the the vertex of `y=(x -4)^2 + 12x -36`?

Answer 1

`y=(x-2)^2-24` is the equation in vertex form.

Explanation:

Vertex form of equation is of the type `y=a(x-h)^2+k`, where `(h,k)` is the vertex and axis of symmetry is `x-h=0`
Here we have

`y=(x-4)^2+12x-36`

`=x^2-8x+16+12x-36`

`=x^2+4x-20`

`=x^2+2xx2x+2^2-4-20`

`=(x-2)^2-24`

Hence, `y=(x-2)^2-24` is the equation in vertex form. Vertex is `(2,-24)` and axis of symmetry is `x-2=0`
graph{(x-2)^2-24-y=0 [-10, 10, -30, 10]}