Question

PLEASE HELP!

Write the quadratic function in the form f (x) = a (x-h)^2+k . Then, give the vertex of its graph.
f (x) = 2x^2 - 12x +16
Writing in the form specified: f ( x) = _
Vertex: ( _ , _ )

Answer 1

complete the square
(h,k) is the vertex

so
f(x)=2x²-12x+16
group x terms
f(x)=(2x²-12x)+16
factor out the 2
f(x)=2(x²-6x)+16
take 1/2 of the linear coefient and square it
-6/2=-3, (-3)²=9
add positive and negative insides parnthases
f(x)=2(x²-6x+9-9)+16
factor perfect square
f(x)=2((x-3)²-9)+16
distribute
f(x)=2(x-3)²-18+16
f(x)=2(x-3)²-2

h=3
k=-2
vertex is (3,-2)
vertex form is f(x)=2(x-3)²-2