Answer
a) $4$ seconds
b) $256~feet$
Work Step by Step
a) Find the $t$ coordinate of the vertex:
$$t=-\frac{b}{2a}=-\frac{128}{2(-16)}=4$$
So, firework explodes after $4$ seconds.
b) Substitute $t=4$ into the function and find $h$:
$$h=-16(4)^2+128(4)=256$$
The firework explodes at $256~feet$
