Finding the coefficient c in a quadratic function

A quadratic function is given by the equation:

$$f(x) = ax^2 + bx + c$$

It is known that the function has a vertex at the point (4, -5), and the coefficient of the $x^2$ term is negative. If the value of $a$ is chosen such that the quadratic opens downwards, what is the value of $c$ if $f(2) = 0$?