What equations would you use for parabolic motion equations such as for horizontal motion, and for vertical motion?

All of the equations used in projectile motion are based on the three basic kinematic equations

v = u + at

v^2 = u^2 + 2ax

x  = ut + (1/2)at^2

in these equations v represents final velocity, u represents initial velocity, a represents acceleration , x represents displacement and t represents time.

So if we apply these equations to the vertical motion we get

Initial vertical velocity = V sin theta

v(y) = v sin theta - gt    where v(t) is the vertical velocity at time t and v is the velocity

                                    of projection. In this case the acceleration is that due

                                     to gravity and is considered negative.

V^2 =( V sin theta)^2 - 2gy

y =  ( V sin theta)t - (1/2)gt^2      where y is vertical displacement

Since gravity does not act horizontally we have for the horizontal motion

Initial Horizontal velocity = V cos theta

V(x)= V cos theta       ( the horizontal velocity never changes )

x  =  ( V cos theta)t