what is the average rate of change for this quadratic function for the interval from x = -4 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, $a=-4$ and $b = - 2$.

Step2: Find $f(-4)$ and $f(-2)$ from the graph

Suppose the $y$-value when $x=-4$ is $y_1$ and when $x = - 2$ is $y_2$. From the graph, assume $f(-4)=0$ and $f(-2)=8$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(-2)-f(-4)}{-2-(-4)}=\frac{8 - 0}{-2 + 4}=\frac{8}{2}=4$.

Answer:

4