What is the vertex form of f(x) ?

Question

Consider the function f, where f(x) = 2x^2 + 6x - 8

What is the vertex form of f(x) ?

A. f(x) = 2(x - 3)^2 - 4

B. f(x) = 2(x + 3)^2 - 4

C. f(x) = 2(x - 1.5)^2 - 1.25

D. f(x) = 2(x + 1.5)^2 - 12.5

Answer 1

2x^2+6x-8

(2x^2+6x)-8

2(x^2+3x)-8

take half of 3 and square it

(3/2)^2=9/4

add 9/4 to x^2+3x but remember you are doubling it

2(x^2+3x+[9/4]) so far

to offset adding 2*(9/4), subtract 2*(9/4) from -8

2(x+[3/2])^2-8-[18/4]

2(x+1.5)^2-8-4.5

2(x+1.5)^2-12.5 which is D.

expand the answer to see that it equals 2x^2+6x-8