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: 75


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

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 $f(x)=0$: $$x^2-50=0$$ Using the Square Root Method $$x^2=50$$ $$ x = \pm \sqrt{50}$$ $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2}$ $$x=\pm 5\sqrt{2}$$ Thus, the zeros, which are also the $x$-intercepts, are $x = 5\sqrt{2},-5 \sqrt{2}$
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