Properties of Parametrically Defined Motion

The particle reaches a horizontal extremum at $t=0$.

The horizontal motion, given by $x(t)=t^2-3*t$, is quadratic and its vertex represents the horizontal extremum.

The vertical motion, described by $y(t)=2*t+1$, is linear, implying a constant vertical velocity.

Differentiating $x(t)$ and $y(t)$ with respect to $t$ provides the components of the particle’s velocity vector.