Question

What is the vertex of `y = (1/4)(4x – 16)^2 - 4`?

Answer 1

Vertex is `(4,-4)`

Explanation:

Vertex form of a parabola is `y = a(x+b)^2+c`

Notice that the coefficient of `x` is 1.

In the question asked, the coefficient of `x` is `4`.

`y = 1/4color(red)((4x-16)^2)-4`

Simplify first: `y= 1/4color(red)((16x^2-128x+256))-4`

Factor out 16:`" "` (the same as `4^2`)

`y= 1/4*16color(blue)((x^2-8x+16))-4" "larr` change to factor form

`y = 4color(blue)((x-4)^2)-4`

(we could have done this in one step at the beginning as long as the factor `4^2` was taken out and not just `4`)

`y = 4(x-4)^2-4` is in vertex form.
The vertex is at `(-b,c)`

Vertex is `(4,-4)`