Algebra: A Combined Approach (4th Edition)

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

Appendix G - Exercise Set - Page 1016: 13

Answer

$f(x) = -2|x-3|+4$ Vertex=(3,4) x-intercepts: (1,0) and (5,0) y-intercept: (0,-2)

Work Step by Step

$f(x) = -2|x-3|+4$ The graph is y=|x| with a dilation of factor $2$ from the x axis, a reflection in the x-axis, and a translation of 3 units in the positive x direction and 4 units in the positive y direction. Thus, the vertex is (3,4). To find the x-intercept, we substitute in y=0. $0 = -2\times|x-3|+4$ $2\times|x-3| = 4$ $|x-3| = 2$ $x-3=2, and -x+3=2$ $x=5, x=1$ Therefore, the x-intercepts are (5,0) and (1,0). To find the y-intercept, we substitute in x=0. $y = -2\times3+4=-2$ Therefore, the y-intercept is (0,-2).
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