Question

Which function in vertex form is equivalent to f(x) = x2 + 8 – 16x?

Answer 1

Answer: The correct option is A.

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 $\frac{b}{2a}$, 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.

Answer 2

The answer would be (f(x) = (x – 8)2 – 56)