Given a quadratic function, f(x) = ax 2 + bx + c has a negative leading coefficient and the vertex that has a negative y-coordinate. determine the number of real zeros of the function.2 real zeros1 real zero1 real zero and 1 imaginary zero2 imaginary zeros

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).

Where is the diagram?