Question

Let f(x)=−14(x+4)2−8 .

What is the average rate of change for the quadratic function from x=−2 to x = 2?

Answer 1

Answer:
Average rate of change = -112

Explanation:
The average rate of change = $\frac{f(b) - f(a)}{b - a}$
where:
b is the upper limit = 2
f(b) = f(2) = -14(2+4)² - 8 = -512
a is the lower limit = -2
f(a) = f(-2) = -14(-2+4)² - 8 = -64

Substitute with these values in the above equation to get the average rate of change as follows:
average rate of change = $\frac{-512 - (-64)}{2 - (-2)} = -112$

Hope this helps :)

Answer 2

The average rate of the function from x = -2 to x = 2 can be calculated as:

$\frac{f(2)-f(-2)}{2-(-2)}$

Using the values, we get:

$\frac{-14(2+4)^{2}-8-[-14(-2+4)^{2}-8] }{4} \\ \\ = \frac{-14(36)-8-[-14(4)-8]}{4} \\ \\ =\frac{-448}{4} \\ \\ =-112$

So, the average rate of change of the given function from x = -2 to x=2 is -112