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: 50


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

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