When making a projectile system, you will find that it is much easier to think in the term of vectors than it is in parabolas. Your projectile will need to have one vector for position (x, y, z) and one for velocity (vx, vy, vz). If you are using vJass, just make a struct for the projectile (will make your life much easier), otherwise use an array for each variable and use some method to find a unique index for each projectile, then use the index to access the array items.
I can totally recommend
this tutorial if you are new to linear algebra and vectors.
When storing the Z cooridnate, it is much easier to use the
absolute height of the unit, i.e.
terrain height + flying height. This way, you can set the fly height to
proj_z[proj_id] - GetTerrainZ(proj_x[proj_id], proj_y[proj_id]). In this case, GetTerrainZ is a custom function where create/move a global location at (x,y) and find the terrain height using GetLocationZ(). This way, you never have to really care about terrain height in your calculations. Just check if
proj_z < terrain_z to see if it collides with the ground.
Every timer cycle, you subtract your Z velocity with a gravity value, which should be something like 10*TIMER_INTERVAL (where TIMER_INTERVAL is something like 0.03). Then, you add the velocity vector to the position vector. Finally, you move your projectile to the position vector. The resulting movement will be parabolic.
EDIT: You can also multiply your velocity vector with something like 0.98 every cycle if you want to add air resistance. This createas a pretty cool effect. If you want to see a projectile system based on these principles, you can check out
SupCom by Bob666, or
World Domination by myself.
Hope this was helpful.
