Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 9 - Quadratic Functions and Equations - Pull it All Together - Page 588: Task 1


Refer to work:

Work Step by Step

The function will have a maximum and open downwards (negative concavity) because the value of $a$ is negative. Because $a$ is less than -1, the function will be more narrow than if $a=-1$. The maximum if $a=-1$ is 3, but since $c$ will be a positive number no matter what value is chosen for $a$, the graph will shift up making its maximum greater than 3. $b$, on the other hand, will always be negative no matter what value is picked for $a$. The zeros for this function will always be the same no matter what value is selected for $a$. $b$ will always be double that of $a$ while staying negative, and $c$ will always be double that of $a$ but positive, or just the opposite value of $b$:
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