5/15 what is the average rate of change of the function q(x) = 2x² - 4x + 7 over the interval 2, 6?

Question

Accepted Answer

# Explanation:
## Step1: Recall the average rate of change formula
The average rate of change of a function $ q(x) $ over the interval $[a, b]$ is given by $\frac{q(b) - q(a)}{b - a}$. Here, $ a = 2 $, $ b = 6 $, and $ q(x)=2x^{2}-4x + 7 $.

## Step2: Calculate $ q(6) $
Substitute $ x = 6 $ into $ q(x) $:
$$
\begin{align*}
q(6)&=2(6)^{2}-4(6)+7\
&=2\times36-24 + 7\
&=72-24 + 7\
&=48 + 7\
&=55
\end{align*}
$$

## Step3: Calculate $ q(2) $
Substitute $ x = 2 $ into $ q(x) $:
$$
\begin{align*}
q(2)&=2(2)^{2}-4(2)+7\
&=2\times4-8 + 7\
&=8-8 + 7\
&=0 + 7\
&=7
\end{align*}
$$

## Step4: Calculate the average rate of change
Using the formula $\frac{q(6)-q(2)}{6 - 2}$, substitute $ q(6)=55 $ and $ q(2)=7 $:
$$
\begin{align*}
\frac{q(6)-q(2)}{6 - 2}&=\frac{55 - 7}{4}\
&=\frac{48}{4}\
&=12
\end{align*}
$$

# Answer:
12

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the average rate of change formula

Step2: Calculate \( q(6) \)

Step3: Calculate \( q(2) \)

Step4: Calculate the average rate of change

Answer: