Which equation describes a parabola that opens up or down and whose vertex is at the point (h v)

The parabola that opens upward has a formula of y = 4ax^2 where a is the length of the latus rectum. When the parabola opens downward, the formula becomes y = -4ax^2. With a vertex of point (h,v), the formulae become y-v = 4a(x-h) ^2 and y-v = -4a(x-h) ^2.