calculating a rate of change of a quadratic function over an interval\nwhich is the rate of change for the…

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-6$ and $b = - 3$.

Step2: Find function values from the graph

From the graph, when $x=-6$, $y = 6$; when $x=-3$, $y = 0$.

Step3: Calculate the rate of change

Substitute into the formula: $\frac{0 - 6}{-3-(-6)}=\frac{-6}{3}=-2$.

Answer:

$-2$