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