Finding the Product of Roots of a Quadratic Function

A quadratic function $f(x)$ is defined by the equation:

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

where $a$, $b$, and $c$ are constants. One day, while analyzing the function, a student finds that when $x = 3$, the value of $f(x)$ is 0, indicating that $3$ is one root of the equation. The function can be rewritten as:

$$f(x) = a(x - 3)(x - r)$$

where $r$ is the other root. After substituting $x = 1$ into the function, the student noted that $f(1) = 12$. Determine the value of the product of the two roots, $3$ and $r$, and express your answer as a decimal.