Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Write an explicit function model from a context and choose a reasonable domain
Problem
Using the motion diagram and \(h(t)=-16t^{2}+32t+4~\text{feet}\), define \(t\) and its units. Solve \(h(t)=0\) exactly, reject the prelaunch root, and state the continuous domain from launch through ground impact with endpoint meanings.
The algebraic roots of the height equation are candidate boundary times, but the motion context begins at launch. We’ll solve the ground-level equation exactly, classify both roots relative to time zero, retain the future impact time, and use the continuously varying launch-to-impact interval as the physical domain.
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