Often you have something like: $$h(t)=-16t^2+V_0t+C$$
I have little experience with parametric equations, but I have also seen parabolic functions represented this way:
$$x=x_0 + V_{0_x}*t$$
$$y=y_0 + V_{0_x}*t-\frac{1}{2}gt^2$$
With a specific example, can someone talk about the connection between the two? When is one format preferable? Does it depend on what initial information you have available? I also want to know how you convert one to the other. etc.
In a sense the first equation is also of 'parametric' form if you consider some parametric variable s, then you get
$$ t = s$$ $$ h = -16s^2 + V_0 t + C$$
Of course, this is a trivial parametrization.
You can convert from the latter to the former. Take the first parametric equation and solve for $t$, you get: $$t=x−x_0 V_0 x$$Substitute this into the expression for $y$, you get $y$ as a function of $x$.
Both forms have their uses, but I find it hard to provide a general "guideline" for when which is optimal, if that's even possible.