Question

What is the average rate of change for this quadratic function for the interval

from x= 2 to x = 4?​

Answer 1

-6

Explanation:

The average rate of a function f(x) on the interval from x=a to x=b is
`(f(b)-f(a))/(b-a)`.

So in the problem you have from
`x=2` to
`x=4`.

The average rate of the function from x=2 to x=4 is

`(f(4)-f(2))/(4-2)=(f(4)-f(2))/(2)`.

Now we need to find f(4) and f(2).

f(4) means what is the y-coordinate that corresponds to x=4 on the curve.

f(4)=-15 since the ordered pair at x=4 is (4,-15).

f(2) means what is the y-coordinate that corresponds to x=2 on the curve.

f(2)=-3 since the ordered pair at x=2 is (2,-3).

So let's plug in those values:

`(f(4)-f(2))/(4-2)=(-15-(-3)))/(2)`.

Now we just simplify:

`(-15+3)/(2)`

`(-12)/(2)`

`-6`