Let the function $$f(x)$$ be defined by the equation:
$$f(x) = ax^2 + bx + c$$
for some constants $$a$$, $$b$$, and $$c$$ where $$a eq 0$$. If it is known that the vertex of the parabola represented by this function lies at the point $$(2, -1)$$, and the function passes through the point $$(4, 3)$$, which of the following is true regarding the values of $$a$$, $$b$$, and $$c$$?