Question

Complete the square to determine the maximum or minimum value of the function defined by the expression -x2-10x+14

Answer 1

Maximum value of the function = 39.

Explanation:

It will have a maximum value because the coefficient of x^2 is negative.

-x2 - 10x + 14

= - (x^2 + 10x) + 14

Completing the square:

= - [(x + 5)^2 - 25)] + 14

Maximum value = -(-25) + 14

= 39 (answer).

Value of x at the maximum = -5.

Answer 2

maximum value = 39

Explanation:

Since the coefficient of the x² term < 0 then function has a maximum value

to complete the square the coefficient of the x² term must be 1

factor out - 1

- (x² + 10x - 14)

add/subtract (half the coefficient of the x- term )² to x² + 10x

= - (x² + 2(5)x + 25 - 25 - 14 )

= - (x + 5)² + 39

The maximum occurs when x = - 5 ⇒ max = 39