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

A. 6

Step-by-step 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.