You can put this solution on YOUR website! solve y^2-x+2y+3=0
complete the square:
(y^2+2y+1)-1-x+3=0
(y+1)^2=x-2
This is an equation of a parabola that opens rightward with vertex at (2,-1)
Its basic equation: (y-k)^2=4p(y-k), (h,k)=(x,y) coordinates of the vertex
see graph below: