Answer
$a$: affects the direction of the graph (and the axis of symmetry)
$b$: affects the axis of symmetry
$c$: the y-intercept of the graph
Work Step by Step
If we let $x=0$, then we have $y=c$ (the y-intercept of the graph).
Depending on whether $a$ is positive or negative, the direction of the graph is affected (opens up or opens down, respectively).
$-b/2a$ determines the axis of symmetry.