Which function in vertex form is equivalent to f(x) = x2 + 8 – 16x? A. f(x) = (x – 8)2 – 56 B. f(x) = (x – 4)2 + 0 C. f(x) = (x + 8)2 – 72 D.f(x) = (x + 4)2 – 32

Question

asked Aug 1, 2018 189k views

2 Answers

Dreams · Answer 1 · 2018-08-07T04:43:07+0000

Answer: The correct option is A.

Step-by-step explanation:

The given function is,

f(x)=x^2+8-16x

Rewrite the above function.

f(x)=(x^2-16x)+8

To make the perfect square we add and subtract the square of
(b)/(2a) , where b is coefficient of x and a is the coefficient of
x^2 .

Since a=1 and b = -16, So we will add and subtract he square of -8.

f(x)=(x^2-16x+(-8)^2)+8-(-8)^2

f(x)=(x^2-16x+(8)^2)+8-64

Using
(a-b)^2=a^2-2ab+b^2

f(x)=(x-8)^2)-56

Therefore, the correct option is A.