Finding x-axis-intercept of a parametric equation and slope

Question

let $x = t^2$ and $y = t^3-3t$

now the equation for the slope is:

$$\frac{dy}{dx} = \frac{3t^2-3}{2t} = 0$$

now at the point (0,0) is the first intercept with the x-axis with slope $\infty$ what is the slope at the second intercept and how to find the second intercept?