Answer
We know $a$ is negative since the graph opens down. We know $c$ is positive since the y-value of $x=0$ is positive.
$b=0$ since the axis of symmetry is $x=0$.
Work Step by Step
Points on the graph: $(1,-2), (-1,-2), (0,1)$
Parabolas with a positive $a$ open up, while a negative $a$ is for a parabola that opens down.
When $x=0$,
$y=ax^2+bx+c$ transforms to
$y=a*0^2+b*0+c$ (which is the same as $y=c$).
Since the maximum value is at $x=0$, we know that $x=0$ is also the axis of symmetry.
$-b/2a = 0$
$-b/2*(-1)=0$
$-b/-2=0$
$b/2=0$
$b=0$
