Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 3 - 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 249: 49


Visually, the parabola intersects the x-axis in two points: $x=-3$ and between $x=0$ and $x=1$. Let's assume that $x=\frac{1}{2}$. The x-intercepts are: $(-3,0)$ and $(\frac{1}{2},0)$ Algebraically: the x-intercepts are $(\frac{1}{2},0)$ and $(-3,0)$

Work Step by Step

$f(x)=0$ $2x^2+5x-3=0~~$ ($a=2,b=5,c=-3$): $x=\frac{-5±\sqrt {5^2-4(2)(-3)}}{2(2)}=\frac{-5±\sqrt {49}}{4}=\frac{-5±7}{4}$ or $x=\frac{2}{4}=\frac{1}{2}$ or $x=-\frac{12}{4}=-3$ x-intercepts: $(\frac{1}{2},0)$ and $(-3,0)$
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