Question

What is the average rate of change for this quadratic function for the intervalfrom x = 0 to x = 2?y5X-55-5

Answer 1

Step-by-step explanation

The question wants us to determine the average rate of change for the given quadratic function

To do so, we will use the formula below

`Average\text{ rate=}(f(x_2)-f(x_1))/(x_2-x_1)`

in our case

`\begin{gathered} x_1=0 \\ x_2=2 \end{gathered}`

So our next step will be to find

`\begin{gathered} f(x_2)\text{ } \\ and \\ f(x_1) \\ \end{gathered}`

From the graph

So that

`\begin{gathered} f(x_1)=f(0)=-6 \\ f(x_2)=f(2)=0 \end{gathered}`

Thus

`Average\text{ rate=}(0-(-6))/(2-0)=(0+6)/(2)=(6)/(2)=3`

Therefore, the average rate is 3