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: 76

Answer

Zeros: $2\sqrt{5},-2\sqrt{5}$ $x$-intercepts: $2\sqrt{5},-2\sqrt{5}$

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 $f(x)=0$: $$x^2-20=0$$ Using the Square Root Method $$x^2=20$$ $$ x = \pm \sqrt{20}$$ $\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2 \sqrt{5}$ $$x=\pm 2\sqrt{5}$$ Thus, the zeros, which are also the $x$-intercepts, are $ x = 2\sqrt{5},-2\sqrt{5}$
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