College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 4 - Section 4.3 - Quadratic Functions and Their Properties - 4.3 Assess Your Understanding - Page 300: 80

Answer

(a) $a = 1: f(x) = (x + 5)(x - 3) = x^2 + 2x - 15$ $a = 2: f(x) = 2(x + 5)(x - 3) = 2x^2 + 4x - 30$ $a = - 2: f(x) = -2(x + 5)(x - 3) = -2x^2 - 4x + 30$ $a = 5: f(x) = 5(x + 5)(x - 3) = 5x^2 + 10x - 75$

Work Step by Step

(a) $a = 1: f(x) = (x + 5)(x - 3) = x^2 + 2x - 15$ $a = 2: f(x) = 2(x + 5)(x - 3) = 2x^2 + 4x - 30$ $a = - 2: f(x) = -2(x + 5)(x - 3) = -2x^2 - 4x + 30$ $a = 5: f(x) = 5(x + 5)(x - 3) = 5x^2 + 10x - 75$ (b) The value of a does not affect the x-intercepts, but it changes the y-intercept by a factor of a. (c) The value of a does not affect the axis of symmetry. It is $x = - 1$ for all values of a. (d) The value of a does not affect the x-coordinate of the vertex. However, the y-coordinate of the vertex is multiplied by a. (e) The mean of the x-intercepts is the x-coordinate of the vertex.
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