For the curve $x=t^2-1,  y=t^2-t$, where the tangent is parallel to x-axis is

t = 0 t → ∞ $t=\frac{1}{\sqrt{3}}$ $t=-\frac{1}{\sqrt{3}}$

t = 0

$\frac{d x}{d t}=2 t$ Tangent is perpendicular to x-axis if $\frac{d x}{d t}=0 \Rightarrow t=0$.