College Algebra, Chapter 4, Chapter Review, Section Review, Problem 14

Graph the polynomial $P(x) = -3 (x + 2)^5 + 96$ by transforming an appropriate graph of the form $y = x^5$ and show all the $x$ and $y$ intercepts clearly.

The graph of $P(x) = -3 (x + 2)^5 + 96$ is obtained from the graph of $y = x^5$ that is shifted $2$ units to the left,
reflected about the $x$ axis and stretched vertically by a factor of $3$. Then, the result is shifted $96$ units upward. To determine the $x$ intercept, we set $y = 0$ so


$\begin{equation} \begin{aligned} 0 =& -3 (x + 2)^5 + 96 \\ \\ 3 (x + 2)^5 =& 96 \\ \\ (x + 2)^5 =& 32 \\ \\ x + 2 =& \sqrt[5]{32} \\ \\ x + 2 =& 2 \\ \\ x =& 0 \end{aligned} \end{equation}$


Next, to determine the $y$ intercept, we set $x = 0$.


$\begin{equation} \begin{aligned} P(0) =& -3 (0 + 2)^5 + 96 \\ \\ =& -3(32) + 96 \\ \\ =& -96 + 96 \\ \\ =& 0 \end{aligned} \end{equation}$


The $y$ intercept is .