## Calculus (3rd Edition)

The curve intersects the x-axis when $t=3$.
The space curve given by $$r(t) = \langle t^2, t^2-2t-3, t-3 \rangle$$ intersects the x-axis when $y=0, z=0$; that is, we have $$t^2-2t-3=0, \quad t-3=0\Longrightarrow t=3.$$ Hence, the curve intersects the x-axis when $t=3$.