Let us not forget that there are two words here. I have ;no idea which came first. The
one refers to the path of a projectele, which would be a perfect mathematical parabola
except for the drag of the atmosphere. The other word is based on paable, a story
told to impart a moral.
And of course, there is the guy with the parabolic chin, a perfect chin to hang a pair on.

parabolic 1
adj.
5LL parabolicus < LGr parabolikos6 of, in the form of, or expressed by a parable: also par#a[bol$i[cal
par#a[bol$i[cal[ly
adv.

parabolic 2
adj.
1 of or like a parabola
2 bowl-shaped, as a reflector, antenna, or microphone, so that sections parallel to the plane of symmetry are parabolas
par#a[bol$i[cal[ly
adv.

If the vertex is at origin and
the x-axis is the axis of the parabola, then take y 2 = 4ax as the equation of parabola.
That is y squared, not y times 2.