College Algebra 7th Edition

Published by Brooks Cole

Chapter 3, Polynomial and Rational Functions - Section 3.2 - Polynomial Functions and Their Graphs - 3.2 Exercises - Page 302: 24

Answer

Refer to the graph below.

Work Step by Step

The $x$-intercepts of the function's graph can be found by equating each factor to zero then solving each equation to obtain: \begin{align*} \frac{1}{5}x&=0 &\text{or}& &(x-5)^2=0\\ x&=0 &\text{or}& &x-5=0\\ x&=0 &\text{or}& &x=5\\ \end{align*} Thus, the $x$-intercepts are $0$ and $5$. The $y$_intercept of the function can be found by setting $x=0$ then solving for $y$: \begin{align*} P(0)&=\frac{1}{5}\cdot0(0-5)^2\\ P(0)&=0\\ \end{align*} Thus, the $y$-intercept is $0$ Create a table of values to obtain the one below. Then, plot each ordered pair and connect the points using a smooth curve. Refer to the graph above.

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