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: 23


Zeros: $\dfrac{3}{2}$ $x$-intercept: $\dfrac{3}{2}$

Work Step by Step

To find the zeros of a function $g$, solve the equation $g(x)=0$ The zeros of the function are also the $x-$intercepts. Let $G(x)=0$: $$4x^2+9-12x=0$$ Rearranging the Equation: $$4x^2-12x+9$$ By Factoring: $$(2x-3)(2x-3)=0$$ Use the Zero-Product Property by equating each unique factor to zero to obtain: $2x-3 = 0$ $2x = 3$ $ x=\dfrac{3}{2}$
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