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

The equation that describes a parabola opening up or down with its vertex at the point ((h, v)) is given by the standard form (y = a(x - h)^2 + v), where (a) determines the direction and width of the parabola. If (a > 0), the parabola opens upward, while if (a < 0), it opens downward. The vertex ((h, v)) is the minimum or maximum point of the parabola, depending on the sign of (a).