Question

Look at the function below. f(x)=−x2−2x+8

Which function is an equivalent form that can be used to identify the maximum value of the function?

a. f(x)=−(x+1)2+7 b. f(x)=−(x+1)2+9 c. f(x)=−(x+2)(x−4) d. f(x)=−(x−2)(x+4)

Answer 1

Answer:

f(x) = -1(x+1)² + 9

Step-by-step explanation:

f(x) = -x² - 2x + 8

This is a down-opening parabola. Put the equation into vertex form. The y-coordinate of the vertex is the maximum.

factor out the leading coefficient

f(x) = -1(x²+2x) + 8

Complete the square

 coefficient of x term: 2

 divide in half: 1

 square it: 1²

 use 1² to complete the square:

f(x) = -1(x²+2x+1²) + 1² + 8

f(x) = -1(x+1)² + 9

vertex (-1,9)

maximum value of f(x) = 9