The curve must have this orientation, since we know it has horizontal axis and passes through (2, -1):

So we need to use the general formula

y² = 4px

We need to find p. We know the curve goes through (2, -1), so we substitute:

(-1)² = 4(p)(2)

→ 1 = 8p

→ p = 1/8.

So the required equation is y² = x/2.