Question

Nature of horizontal projectile is parabolic

Answer 1

nature of projectile is parabolic because the vertical position of the object is influenced only by a constant acceleration, (if constant drag etc. is also assumed) and also because horizontal velocity is generally constant.

Answer 2

vertical component of projectile is influced by gravity of earth decreases vertical acceleration
vertical compent of projectile remains constant.
So nature of projectile is parabolic.