$y^2$ = 4ax opens right (focus on positive x-axis). $y^2$ = -4ax opens left. $x^2$ = 4ay opens up. $x^2$ = -4ay opens down. In all cases, the vertex is at origin and the latus rectum length is 4a. For shifted parabolas, replace x with (x-h) and y with (y-k) to shift the vertex to (h,k). The general equation of a parabola with axis parallel to a coordinate axis involves either $x^2$ or $y^2$ (not both).