Determine the Value of a Quadratic Function

Let the function $$ f $$ be defined by the equation:

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

where $$ a $$, $$ b $$, and $$ c $$ are constants. If it is given that $$ f(1) = 1 $$ and $$ f(2) = 5 $$, determine the value of $$ f(3) $$.