complete the square y^2+6y-3x+3=0
y^2 + 6 y = 3 x - 3
y^2 + 6 y + 9 = 3 x + 6
(y+3)^2 = 3 x + 6
(y+3)^2 = 3 (x+2)
vertex at (-2,-3) open to right
y^2 + 6 y + 9 = 3 x + 6
(y+3)^2 = 3 x + 6
(y+3)^2 = 3 (x+2)
vertex at (-2,-3) open to right