jmc

The vertex of the parabola is $(-3,1)$, so the equation of the parabola is of the form $$x=a(y-1{)}^2-3.$$ The parabola passes through the point $(-2,2)$. Substituting these values into the equation above, we get $$-2=a(2-1{)}^2-3.$$ Solving for $a$, we find $a=1$. Hence, the equation of the parabola is given by $$x=(y-1{)}^2-3=(y^2-2y+1)-3=y^2-2y-2.$$ The answer is $1-2-2=\boxed{-3}$.

Alternatively, note that $a+b+c$ is the value of $a{y}^2+by+c$ when $y=1$. The parabola passes through the point $(-3,1)$, so $a+b+c=\boxed{-3}$.