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: 44

Answer

a) See graph b) Domain $(-\infty, \infty)$ Range$ [-1.25, -\infty)$ c) Increasing $(-\infty, 0.5]$ Decreasing $[0.5, \infty)$

Work Step by Step

$f(x) = -3x^2 + 3x - 2$ a) $a = -3$, $b = 3$, $c = -2$ a < 0, so graph will open down vertex $x = \frac{-b}{2a} = 0.5$ Axis of symmetry $x = 0.5$ Maximum value = $f(0.5) = -3(0.5)^2 +3 \times 0.5 -2 = -1.25$ For x intercept $y = 0$ we get $-3x^2 + 3x - 2 = 0$ =>Discriminant of quadratic is negative(-15) so no x-intercepts y-intercept at $x = 0$, $(0, -2)$ b) Domain $(-\infty, \infty)$ Range$ [-1.25, -\infty)$ c) Increasing $(-\infty, 0.5]$ Decreasing $[0.5, \infty)$
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