question given the function h(x)=-x² - 5x + 11, determine the average rate of change of the function over…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = h(x)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$, where $a=-8$ and $b = 4$.

Step2: Calculate $h(-8)$

Substitute $x=-8$ into $h(x)=-x^{2}-5x + 11$. $h(-8)=-(-8)^{2}-5\times(-8)+11=-64 + 40+11=-13$.

Step3: Calculate $h(4)$

Substitute $x = 4$ into $h(x)=-x^{2}-5x + 11$. $h(4)=-4^{2}-5\times4+11=-16-20 + 11=-25$.

Step4: Calculate average rate of change

$\frac{h(4)-h(-8)}{4-(-8)}=\frac{-25-(-13)}{4 + 8}=\frac{-25 + 13}{12}=\frac{-12}{12}=-1$.

Answer:

$-1$