Finding the Constant c in a Quadratic Function

Consider a function defined by the equation:

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

Where $a$, $b$, and $c$ are constants. It is known that the vertex of this parabola is located at the point $(-3, 2)$. Additionally, the function passes through the point $(0, 1)$.

Determine the value of $c$.