Function Transformation Evaluation

Consider the function $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants. The function is transformed to $g(x) = f(x + 1) - f(x)$. You are given that $f(0) = 3$, $f(1) = 7$, and $f(2) = 13$. Based on this information, determine the value of $g(0)$. Which of the following options is correct?