The function would be h(t)=-16t²+v₀t+0, where v₀ is the initial velocity of the firework.
0 is the initial height, since you cannot hold one in your hand and safely set it off.
This will have a maximum; the firework will reach a highest point and fall back down. This is also evident from the equation; the negative in front of t² flips the parabola upside down, which gives it a maximum.
