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 - Page 312: 6


$5$; 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
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.