Chapter 9 - Quadratic Functions and Equations - 9-1 Quadratic Graphs and Their Properties - Practice and Problem-Solving Exercises - Page 540: 50

a) either both $a$ is positive and $c$ is negative or both $a$ is negative and $c$ is positive. b) either both $a$ and $c$ are positive or both $a$ and $c$ are negative.

a) When both $a$ is positive and $c$ is negative, the graph opens up and has its vertex below the x-axis. When both $a$ is negative and $c$ is positive, the graph opens down and has its vertex above the x-axis. b) When both $a$ and $c$ are positive, the graph opens up and has its vertex above the x-axis. When both $a$ and $c$ are negative, the graph opens down and has its vertex below the x-axis.