Question

Let f(x)=−1/4(x+4)^2−8 . What is the average rate of change for the quadratic function from x=−2 to x = 2? Enter your answer in the box.

Answer 1

Answer:

Average rate of change of function is -2.

Step-by-step explanation:

Given $f(x)=\frac{-1}{4}(x+4)^2-8$.

we have to find the average rate of change for the quadratic function from x=−2 to x = 2.

$f(-2)=\frac{-1}{4}(-2+4)^2-8=\frac{-1}{4}(4)-8=-9$

$f(2)=\frac{-1}{4}(2+4)^2-8=\frac{-1}{4}(36)-8=-17$

The average rate of change of the function  f(x) on interval [-2,2] is

$\frac{f(b)-f(a)}{b-a}=\frac{f(2)-f(-2)}{2-(-2)}=\frac{-17-(-9)}{4}=\frac{-8}{4}=-2$