First, for clarity, please use " ^ " to denote exponentiation: f(x) = ax^2 + bx + c.
Given: a<0
vertex has a negative y-coordinate => f(x) is negative at the vertex.
What can we learn about the discriminant here? Consider b^2 - 4(a)(c).
b^2 is always positive. If a is <0 (as we were told that it is), and if c>0, then b^2 - 4ac will be positive, and because of that, the TWO roots will be real, whether equal or unequal.
However, if c<0, that conclusion no longer holds; you'd have two complex roots (or two imaginary roots).
