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
1 answer:
Answer:
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.
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