College Algebra, Chapter 3, 3.4, Section 3.4, Problem 12

A function $\displaystyle f(z) = 1 - 3z^2$. Determine the average rate of change of the function between $z = -2$ and $z = 0$.


$
\begin{equation}
\begin{aligned}

\text{average rate of change } =& \frac{f(b) - f(a)}{b - a}
&& \text{Model}
\\
\\
\text{average rate of change } =& \frac{f(0) - f(-2)}{0 - (-2)}
&& \text{Substitute } a = -2 \text{ and } b = 0
\\
\\
\text{average rate of change } =& \frac{1 - 3(0)^2 - [1 - 3(-2)^2]}{2}
&& \text{Simplify}
\\
\\
\text{average rate of change } =& \frac{1 - 1 + 12}{2}
&& \text{Combine like terms}
\\
\\
\text{average rate of change } =& \frac{12}{2}
&& \text{Simplify}
\\
\\
\text{average rate of change } =& 6
&& \text{Answer}

\end{aligned}
\end{equation}
$