Question

What is the average rate of change for this quadratic function for the interval from x=-5 to x=-3?

Answer 1

Answer: OPTION C.

Explanation:

You need to use this formula:

`averate\ rate\ of\ change=(f(b)-f(a))/(b-a)`

Knowing that we need to find the average rate of change for the given quadratic function, for the interval from
`x=-5` to
`x=-3`, we need to find their corresponding y-coordinates.

We can observe in the graph that:

For
`x=b=-5` →
`y=f(b)=-15`

For
`x=a=-3` →
`y=f(a)=1`

Therefore, substitituting, we get:

`averate\ rate\ of\ change=(-15-1)/(-5-(-3))=8`

Answer 2

C 8

Explanation:

The average rate of change is given by

f(x2) -f(x1)

---------------

x2-x1

x2 = -3 and x1 = -5

Looking at the graph

f(x2) = f(-3) = 1

f(x1)= f(-5) =-15

Substituting these values into the equation

1 - (-15)

---------------

-3 - (-5)

1+15

----------

-3 +5

16

----

2

8