College Algebra, Chapter 4, 4.2, Section 4.2, Problem 20

Sketch the graph of polynomial function $\displaystyle P(x) = \frac{1}{5}x (x - 5)^2$ make sure the graph shows all intercepts and exhibits the proper end behaviour.
The function has an odd degree 3 and a positive leading coefficient. Thus, its end behaviour is $y \rightarrow -\infty \text{ as } x \rightarrow -\infty \text{ and } y \rightarrow \infty \text{ as } x \rightarrow \infty$.
To solve for the $x$-intercept, we set $y = 0$.


$
\begin{equation}
\begin{aligned}
0 &= \frac{1}{5}x (x - 5)^2\\
\\
0 &= x \quad \text{and} \quad (x - 5)^2 = 0
\end{aligned}
\end{equation}
$


We have,
$x = 0$ and $x = 5$

To solve for the $y$-intercept, we set $x = 0$
$\displaystyle y = \frac{1}{5} (0) (0 - 5)^2 = 0$