Every quadratic equation has two roots. So the statement of the problem should say that the function has at least one REAL zero.
The vertex is (h,b); a < 0 means the parabola opens downward.
If the equation has at least one zero and the parabola opens downward, then the vertex must be on or above the x-axis.
But there is no other information given; so b can be any number greater than or equal to 0.
