If the trajectory of a body is parabolic in one frame, can it be parabolic in another frame that moves with a constant velocity with respect to the first frame? If not, what can it be?

Explanation

If the trajectory of a body is parabolic with reference frames one and two then those two frames are of rest or moving with uniform velocity.
If they are not parabolic then for that reference frame it may be in straightline path.
Ex: when a body is dropped from a moving plane its path is parabolic for a person outside the plane .But for the pilot in the plane it is falling vertically downwards.