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

1 Answer
Apr 15, 2017

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)