what is the average rate of change for this quadratic function for the interval from x = 0 to x = 2?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b = 2$.

Step2: Find $f(0)$ and $f(2)$ from the graph

From the graph, when $x = 0$, the $y$-value (i.e., $f(0)$) is 8. When $x=2$, the $y$-value (i.e., $f(2)$) is 0.

Step3: Calculate the average rate of change

Substitute $a = 0$, $b = 2$, $f(0)=8$, and $f(2)=0$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(2)-f(0)}{2 - 0}=\frac{0 - 8}{2}=\frac{-8}{2}=-4$.

Answer:

B. -4