what is the average rate of change for this quadratic function for the interval from x = 2 to x = 4?

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, $a = 2$, $b = 4$.

Step2: Read function values from the graph

From the graph, when $x = 2$, assume the $y$-value (let's say $y_1$) is $- 5$. When $x = 4$, assume the $y$-value (let's say $y_2$) is $-5$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{y_2 - y_1}{4 - 2}=\frac{-5-(-5)}{4 - 2}=\frac{-5 + 5}{2}=\frac{0}{2}=0$.

Answer:

$0$