#### Answer

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.

#### Work Step by Step

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.