Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 2 - Linear and Quadratic Functions - Section 2.3 Quadratic Functions and Their Zeros - 2.3 Assess Your Understanding - Page 146: 71


Zeros: $0,16$ $x$-intercepts: $0,16$

Work Step by Step

To find the zeros of a function $f$, solve the equation $f(x)=0$ The zeros of the function are also the $x-$intercepts. Let $G(x)=0$: $$x-4\sqrt{x}=0$$ Let $u=\sqrt{x}$, the original equation becomes $$u^2-4u=0$$ By factoring $$u(u-4) = 0$$ Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain: \begin{align*} u &= 0 &\text{ or }& &u-4=0\\ u &= 0 &\text{ or }& &u=4\\ \end{align*} To solve for $x$, we use $u=\sqrt{x}$ $$\because u=\sqrt{x}$$ $$\therefore x =u^2$$ For $u=0$ $$x=(0)^2 $$ $$x= 0$$ For $u=4$ $$x=(4)^2$$ $$x= 16$$ $\therefore x =0,16$
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