What would be the best method to find the parametric equations for the parabola $y = (x-2)^2$ over a given domain of $(2 ≤ t ≤ 5)$?
The figure I've been given has the parabola starting from $(2,0)$ and ending at $(5,9)$.
I need to find both $x(t)$ and $y(t)$, is there an easy was of doing this?
Since the set $\{ (x,y) \in \mathbb{R}^{2} \mid y = (x-2)^{2} \}$ is the parabola under consideration, if $\varphi: t \mapsto (t, (t-2)^{2})$ on $[2,5]$ then $\varphi[2,5]$ is the segment of the parabola joining $(2,0)$ and $(5,9)$.