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

B) maximum at 15

Step-by-step 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.