sends a firework display high into the sky

shoot up abruptly, like a rocket; "prices skyrocketed"

A skyrocket is a type of firework that uses a solid rocket motor to rise quickly into the sky. At the apex of its ascent, it is usual for a variety of effects (stars, bangs, crackles, etc.) to be emitted. Sky rockets use various stabilisation techniques to ensure the flight follows a predictable course, often a long stick attached to the side of the motor, but also including spin-stabilisation or fins.