Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.2 Linear and Quadratic Functions - Exercises - Page 19: 48


(a) True (b) False

Work Step by Step

First of all because it is given that f(x) is a quadratic function , its graph is a parabola. (a) this is true. because f(x)-c is a vertical transltion of graph of f(x), there is only one and one value of c that will move the vertex of the parabola to the axis. (b) this is false. because f(x-c) is a horizontal translation of the graph of f(x). if f(x) has a double root, then f(x-c) will have a double root of any value of c; on the other hand if f(x) does not have a double root, then there is no value of c for which f(x-c) will have a double root.
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