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It is given by

y = xtanФ(1 - x/R)

where y = height attained

x = horizontal distance

R = total range of the projectile

Ф = Angle of projection

horizontal motion is uniform motion

the distance travelled by the projectile in time ' t'

x= vcosФt

t= x/v cosФ ........ 1

vertical motion is uniformly accelerated motion

distance travelled by the particle in vertical direction in time 't' is

using (s=ut+1/2at²)

y=vsinФt - 1/2 gt² ...........2

from 1 and 2

y= vsinФ× x/cosФ - 1/2 g x²/v²cos²Ф

y= x tanФ - 1/2 g x²/v²cos²Ф

yαx²

hence the projectile is parabolic in nature.