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Question 5

The equation for the fireworks' height is $h(t) = -16t^2 + 80t$.
Task: Find the domain of the function.

• The domain is determined by when the object is launched (at $t = 0$) and when it hits the ground ($h(t) = 0$).

1. Set $h(t) = 0$:
   $-16t^2 + 80t = 0$
   Factor:
   $t(-16t + 80) = 0 \implies t = 0 \text{ or } t = 5 \, \text{seconds}.$

2. The domain is from $t = 0$ to $t = 5$, i.e.,