For b, the sign relates to whether the derivative's y-intercept was positive or negative. So I would say, the graph reaches a maximum at x=0, therefore the derivative has y=0 when x=0. Therefore b=0.
For a, the sign of a relates to whether the parabola opens up or down, and also whether the line's slope is positive or negative (respectively). So I would say, the function increases on the right and decreases on the left, implying that the derivative goes from negative to positive values from left to right. Since the derivative is a line, it has constant positive slope; that is, 2a>0. So a is positive.
It seems a little artificial, but the question is rather artificial, so I'd run with it.