You can get a nice parabolic smoothing by having a "height map" particle move across the screen with applied random gravity.  If the velocity gets too positive, make the gravity negative and if the velocity is too negative, make gravity positive.  Also, have the gravity flip at random intervals.  That gives a very smooth curve that resembles random wave motion in a cool way.

Ok...  because of my unfamiliarity with Axe's system of numbers I decided to try in BASIC first; I managed to make it work but not in axe: it produces a bunch of random vertical lines

BASIC version
:ClrDraw
:0->Xmin
:0->Ymin
:94->Xmax
:62-.Ymax
:8->V
:5->G
:0->A
:40->L2(1
:For(X,1,94
:L2(x)-2GA/V^2->L2(x+1)
:A+1->A
:If 2<abs(-2GA/V^2
:Then
:-G+randInt(-2,2->G
:-9->A
;End
:End
;For(A,1,94
:Line(A,L2(A),A+1,L2(A+1)
:End
And then I changed it to match Axe syntax:
:.AMAP
:ClrDraw
:8->V
:5->G
:0->A
:deltaList(40)->GDB1
:For(X,1,94
:-2*G*A//V//V+{X+GDB1}->{GDB1+X+1
:A+1->A
:If 2<abs(-2*G*A//V//V
:-G->G
:-9->A
;End
:End
:For(A,0,94
:Line(A,{GDB1+A},A+1,{GDB1+A+1
:End
;DispGraph
;Repeat getKey
:End
The basic idea is to just change the Y value by the derivative of the equ gx^2/v^2 + y where g= grav. constant, v=intitial velocity, and y= initial height and flip the gravity when f'x>2