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

2 Answers
Jul 10, 2018

Vertex (4, -4)

Explanation:

Given -

y=2(x/2-2)^2-4

y=2(x^2/4-2x+4)-4

y=1/2 x^2-4x+8-4

y=1/2 x^2-4x+4

Vertex -

x=(-b)/(2a)=(-(-4))/(2 xx 1/2)=4/1=4

At x=4; y=2(4/2-2)^2-4=2(0)-4=-4

Vertex (4, -4)

(4, -4)

Explanation:

Given equation,

y=2(x/2-2)^2-4

y=2(\frac{x-4}{2})^2-4

y=1/2(x-4)^2-4

y+4=1/2(x-4)^2

(x-4)^2=2(y+4)

The above equation shows a vertical parabola with vertex

(x-4=0, y+4=0)

(x=4, y=-4)

(4, -4)