given the function ( h(x) = -x^{2}-5x + 9 ), determine the average rate of change of the function over the interval ( -8leq xleq2 ).

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
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 $h(x)=-x^{2}-5x + 9$.
$$
\begin{align*}
h(-8)&=-(-8)^{2}-5\times(-8)+9\
&=-64 + 40+9\
&=-15
\end{align*}
$$
## Step3: Calculate $h(2)$
Substitute $x = 2$ into $h(x)=-x^{2}-5x + 9$.
$$
\begin{align*}
h(2)&=-(2)^{2}-5\times(2)+9\
&=-4-10 + 9\
&=-5
\end{align*}
$$
## Step4: Calculate the average rate of change
Substitute $h(-8)=-15$, $h(2)=-5$, $a=-8$, and $b = 2$ into the formula $\frac{h(b)-h(a)}{b - a}$.
$$
\begin{align*}
\frac{h(2)-h(-8)}{2-(-8)}&=\frac{-5-(-15)}{2 + 8}\
&=\frac{-5 + 15}{10}\
&=\frac{10}{10}\
&=1
\end{align*}
$$

# Answer:
$1$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \(h(-8)\)

Step3: Calculate \(h(2)\)

Step4: Calculate the average rate of change

Answer: