Continuity of a Piecewise Function

Consider the function $g(x) = \begin{cases} ax^2 + bx + c, & x < 1 \\ 2x-3, & x \geq 1 \end{cases}$. Given that $g$ is continuous at $x = 1$, with $g(1) = -1$ and $g'(1) = 2$, what is the value of $a + b + c$?