Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Review - Page 832: 53

Answer

Vertex: $(-5/6, 73/12)$ Opens downward x-intercepts: -2.3, .6 y-intercept: 4

Work Step by Step

$f(x)=-3x^2-5x+4$ $a=-3$, $b=-5$, $c=4$ $x=-b/2a$ is the vertex. $x=-b/2a$ $x=-(-5)/2(-3)$ $x=5/-6$ $x=-5/6$ $f(x)=-3x^2-5x+4$ $f(-5/6)=-3(-5/6)^2-5(-5/6)+4$ $f(-5/6)=-3*25/36+25/6+4$ $f(-5/6)=-75/36+25/6+4$ $f(-5/6)=-25/12+49/6$ $f(-5/6)=-25/12+98/12$ $f(-5/6)=73/12$ Since the $x^2$ coefficient is negative, the graph opens downward. $x=0$ $f(x)=-3x^2-5x+4$ $f(0)=-3*0^2-5*0+4$ $f(0)=-3*0-0+4$ $f(0)=0+4$ $f(0)=4$ $y=0$ $f(x)=-3x^2-5x+4$ $0=-3x^2-5x+4$ $a=-3$, $b=-5$, $c=4$ $x=(-b±\sqrt {b^2-4ac})/2a$ $x=(-(-5)±\sqrt {(-5)^2-4*-3*4})/2*(-3)$ $x=(5±\sqrt {25+48})/-6)$ $x=(5±\sqrt {73})/-6)$ $\sqrt {73} = 8.5$ $x=(5±\sqrt {73})/-6)$ $x=(5±8.5)/-6$ $x=(5+8.5)/-6$ $x=13.5/-6$ $x=-2.25$ $x=-2.3$ $x=(5-8.5)/-6$ $x=-3.5/-6$ $x=7/12$ $x=.59$ $x=.6$
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