the graph shows the quadratic function $f(x)$. what is the average rate of change for the quadratic function…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$ and $b=8$.

Step2: Read function values from the graph

From the graph, when $x = 4$, $f(4)=10$; when $x = 8$, $f(8)=6$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(8)-f(4)}{8 - 4}=\frac{6 - 10}{8 - 4}=\frac{-4}{4}=-1$.

Answer:

$-1$