Quadratic Function Evaluation

Let the function $f(x)$ be defined as follows:

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

where $a$, $b$, and $c$ are constants.

Assume that $f(1) = 4$, $f(2) = 7$, and $f(3) = 12$. What is the value of $f(4)$?