Interpret key graph/table features of quadratic models in context.
Find the contextual domain of a quadratic model from the situation
Problem
The height of an object after launch is modeled by \(h(t)~=~-16t^2~+~64t\), where \(t\) is time in seconds. Identify the contextual domain from launch until landing.
Big Picture
What this problem is really about
A contextual domain is bounded by the inputs for which the modeled event is actually happening, not by every input the formula accepts. We’ll solve for the ground-level boundary times, identify their roles in the motion, and decide endpoint inclusion from whether those boundary events belong to the flight.
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