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

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


`(f(2)-f(-2))/(2-(-2))`

Using the values, we get:


`(-14(2+4)^(2)-8-[-14(-2+4)^(2)-8] )/(4) \\ \\ = (-14(36)-8-[-14(4)-8])/(4) \\ \\ =(-448)/(4) \\ \\ =-112`

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

Answer 2

Answer:
Average rate of change = -112

Step-by-step explanation:
The average rate of change =
`(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 =
`(-512 - (-64))/(2 - (-2)) = -112`

Hope this helps :)