Hi everyone, I received this problem in my Calculus 2 class today as a bonus problem and I don't know how to proceed on it:

---

A bead is sliding on a wire having position x(t) = (2-3t)^2, y(t) = 2-3t. If the bead slides off the wire at time t=1, where is it when t=3?

---

So far I've found that at t = 1, the point on the wire is (1,-1). Eliminating t in the parametric equation leaves the equation x = y^2 which is a parabola opening to the right. The first derivative should be 2y, which means the velocity at t = 1 should be 2. What I don't know is what path the bead will take after it slides off the wire and what to do after that.

Any help will be greatly appreciated, thanks