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. $-b/2a = 0$ $-b/2*(-1)=0$ $-b/-2=0$ $b/2=0$ $b=0$