Question

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

Answer 1

Answer:

-6

Step-by-step explanation:

The average rate of a function f(x) on the interval from x=a to x=b is $\frac{f(b)-f(a)}{b-a}$.

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

$\frac{f(4)-f(2)}{4-2}=\frac{f(4)-f(2)}{2}$.

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:

$\frac{f(4)-f(2)}{4-2}=\frac{-15-(-3))}{2}$.

Now we just simplify:

$\frac{-15+3}{2}$

$\frac{-12}{2}$

$-6$