Tilted Parabolic Slide

A massive bead is positioned on a parabolic wire in the $xy$ -plane with the following parametrization (all distances in meters): $\begin{aligned} \vec{P} = (x,y) &= \alpha\, \vec{v_1} + \alpha^2\, \vec{v_2} \\ \vec{v_1} &= \left(\frac{\sqrt{3}}{2},-\frac{1}{2} \right) \\ \vec{v_2} &= \left(\frac{1}{2},\frac{\sqrt{3}}{2} \right). \end{aligned}$ There is an ambient gravitational acceleration of $10\text{ m/s}^2$ in the $-y$ direction. The bead starts from rest at $\alpha = -1$ , slides without losses along the wire, and leaves the wire at $\alpha = +1$ .

What is the bead's $x$ -coordinate when it crosses the $x$ -axis for the first time after leaving the wire?