Answer
It is correct.
Work Step by Step
The parabolic description of the path would be exact if the Earth were flat and the acceleration were constant, which is an approximation that generally holds true for projectiles.
However, strictly speaking, according to Kepler’s first law, the projectile is orbiting the Earth in an elliptical orbit. It is an ellipse where the major axis is much larger than the minor axis, and a small arc of it is very close to a parabola.
