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)#