Question

Complete the square to determine the maximum or minimum value of the function defined by the expression.

−x2^2 − 6x + 6

A) minimum value at 3

B) maximum value at 15

C) minimum value at −1

D) minimum value at −6

Answer 1

B) maximum at 15

Explanation:

Factor the leading coefficient from the first two terms.

-(x^2 +6x) +6

Add the square of half the x-coefficient inside parentheses and subtract the same quantity outside.

-(x^2 +6x +9) +6 -(-9)

-(x +3)^2 +15

Compared to the form

a(x -h)^2 +k

we find a=-1, h=-3, k=15. The negative vertical scale factor (a=-1) means the parabola opens downward. The vertex is located at (h, k) = (-3, 15).

The maximum value is 15.