Fragments of fireworks beautifully illuminate the night sky. what specific path is ideally traced by each fragment?

When a certain particle is shot in sky at some angle, it behaves as a projectile. The path travelled by a projectile is parabolic in nature.

If there is no gravity, it will travel along the path or direction to which it is shot.

a)

Fragments of fireworks are blown apart from the firework at some angle and gravity  acts on them, it tries to pull them down.

Therefore, fragments follow a parabolic path.