Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Review Exercises - Page 430: 31


$x=-5$ (multiplicity 1), crosses the x-axis. $x=5$ (multiplicity 2), touches the x-axis and turns around.

Work Step by Step

Step 1. Factor the given function as $f(x)=x^2(x-5)-25(x-5)=(x-5)^2(x+5)$ Step 2. We can identify its zeros as $x=-5$ (multiplicity 1) and $x=5$ (multiplicity 2). Step 3. For $x=-5$, the graph crosses the x-axis. Step 4. For $x=5$, the graph touches the x-axis and turns around.
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