A Parabola Through Four Moves

Starting with the parabola $y = x^2 + 2x + 4$, the graph was: • reflected about the $x$-axis • translated 3 units to the right • reflected about the $y$ axis • translated 3 units up in that order. The resulting graph represents the parabol $y = ax^2 + bx + c$. Determine the value of $a+b+c$.