The "general" form of a parabola's equation is the one you're used to, y = ax^{2} + bx + c—

unless the quadratic is "sideways"

in which case the equation will look something like x = ay^{2} + by + c.

The important difference in the two equations is in which variable is squared: for regular (vertical) parabolas, the x part is squared; for sideways (horizontal) parabolas, the y part is squared.