Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 3 - Polynomial and Rational Functions - 3.1 Quadratic Functions and Models - 3.1 Execises: 6

Answer

$5$; two

Work Step by Step

RECALL: The quadratic function $f(x) = ax^2+bx+c$ opens: (a) downward when $a \lt0$; or (b) upward when $a\gt0$. The given quadratic function has $a=-2$. Thus, its graph is a parabola that opens downward. The y-intercept of the function can be found by setting $x=0$ then solving for $f(0)$: $f(x)=-2x^2-6x+5 \\f(0) = -2(0^2)-6(0)+5 \\f(0) = 5$ The y-intercept is $(0, 5)$. The parabola opens downward. Having a y-intercept of $(0, 5)$, which is above the x-axis, means that the vertex is also above the x-axis. A parabola that opens downward and whose vertex is above the x-axis will cross the x-axis at two points. Thus, the function has 2 x-intercepts. Therefore, the missing expressions in the given statement are (in order): $5$; two
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