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

Explanation:

Step1: Identify the formula for rate of change

The rate of change of a function over an interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here $x_1=-6$ and $x_2 = - 3$.

Step2: Find the function - values from the graph

From the graph, when $x=-6$, $y = 6$ (so $f(-6)=6$), and when $x=-3$, $y=-1$ (so $f(-3)=-1$).

Step3: Calculate the rate of change

Substitute into the formula: $\frac{f(-3)-f(-6)}{-3-(-6)}=\frac{-1 - 6}{-3 + 6}=\frac{-7}{3}=-\frac{7}{3}$.

Answer:

$-\frac{7}{3}$