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
[tex]Average\text{ rate=}\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
in our case
[tex]\begin{gathered} x_1=0 \\ x_2=2 \end{gathered}[/tex]
So our next step will be to find
[tex]\begin{gathered} f(x_2)\text{ } \\ and \\ f(x_1) \\ \end{gathered}[/tex]
From the graph
So that
[tex]\begin{gathered} f(x_1)=f(0)=-6 \\ f(x_2)=f(2)=0 \end{gathered}[/tex]
Thus
[tex]Average\text{ rate=}\frac{0-(-6)}{2-0}=\frac{0+6}{2}=\frac{6}{2}=3[/tex]
Therefore, the average rate is 3
