$$ \vec{r}(t) = \langle t, t^2 \rangle $$
$$ \vec{r}(t) = \langle 2-t^2, t \rangle $$
$$ \vec{r}(t) = \langle 1-t, t \rangle $$
$$ \vec{r}(t) = \langle t, 2t+1 \rangle $$
$$ \vec{r}(t) = \langle t, 2 \rangle $$
$$ \vec{r}(t) = \langle 3, t \rangle $$