Apply quadratic functions to physical situations such as projectile motion under gravity.
Determine the meaningful range for a projectile model over a given domain
Problem
Determine the meaningful range for projectile model \(h(t)=-16t^2+64t\) over domain \(0~\le~t~\le~4\).
Big Picture
What this problem is really about
The meaningful range is built from height outputs over the stated flight-time domain, not from the time endpoints themselves. We’ll evaluate both endpoints and the interior vertex, identify the attained minimum and maximum, and use continuity to include every height between them.
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