Finding Values of Quadratic Function

Let function $f$ be defined by the equation $$f(x) = ax^2 + bx + c$$ for real coefficients $a$, $b$, and $c$. If the function has its vertex at the point $(2, -3)$, and it passes through the point $(0, 1)$, determine the value of $f(4)$.

Recall that a quadratic function can be expressed in vertex form as $$f(x) = a(x-h)^2 + k$$ where $(h, k)$ is the vertex of the parabola.