A parabola opening up or down has vertex (0,0) and passes through (6,–3). Write its equation in vertex form.

Answer 1

Given that the vertex of the parabola is at the origin (0, 0), it must be either in the form of x² or -x². Since it passes through (6, -3), the parabola must open down to go through a negative y-value. Since it opens down, the equation must be in the form of -x². To determine the coefficient ('a') in front of the x²-value, use the coordinate as follows:

-3 = -a (6)²

-3 = -a (36)

-3/-36 = a

a = 1/12

So the equation is y = -1/12 x².

Answer 2

General Vertex Form: y = a(x - h)² + k

Vertex: (h, k) → (0, 0)

y = a(x - 0)² + 0

y = ax²

We are given a point at (6, -3). Plug in the values to find a.

-3 = a(6)2 → -3 = 36a → a = -1/12 (The parabola will open down since a < 0)

y = (-1/12)x²