Question

if Lylah completes the square for f(x)=x squared -12x+7 in order to find the minimum she must write f(x) in the general form f(x)=(x-a)squared +b what is the value of a for f(x)? A. 6 B. -6 C. 12 D. -12 ​

Answer 1

A. 6

Explanation:

f(x) = x² − 12x + 7

To complete the square, we first factor the leading coefficient to make it 1 (which it already is).

Then, we take half the second coefficient, square it, and then add to both sides. So (-12/2)² = (-6)² = 36.

f(x) + 36 = x² − 12x + 36 + 7

Then we factor the perfect square:

f(x) + 36 = (x − 6)² + 7

Then solve for f(x) by subtracting and simplifying:

f(x) = (x − 6)² + 7 − 36

f(x) = (x − 6)² − 29

So the value of a is 6.