question given the function h(x)=-x² - 8x + 18, 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 $\frac{h(b)-h(a)}{b - a}$. Here, $a=-8$ and $b = 2$.

Step2: Calculate $h(-8)$

Substitute $x=-8$ into $h(x)=-x^{2}-8x + 18$. $h(-8)=-(-8)^{2}-8\times(-8)+18=-64 + 64+18=18$.

Step3: Calculate $h(2)$

Substitute $x = 2$ into $h(x)=-x^{2}-8x + 18$. $h(2)=-2^{2}-8\times2+18=-4-16 + 18=-2$.

Step4: Calculate the average rate of change

$\frac{h(2)-h(-8)}{2-(-8)}=\frac{-2 - 18}{2 + 8}=\frac{-20}{10}=-2$.

Answer:

$-2$