Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.
Interpret a quadratic graph feature in context
Problem
Ball height \(H(t)\), in feet, is modeled for \(0~\le~t~\le~6\) seconds and has global maximum vertex \((3,~80)\). Interpret the input, output, extremum, and behavior in context, including the corresponding function statement.
Big Picture
What this problem is really about
A contextual vertex combines an input event, an output quantity, and an extremum claim. We’ll assign the correct meanings and units to the two coordinates, translate the point into function notation, and check that it lies within the modeled time interval. The parabola’s opening then tells how the quantity changes before and after that event without confusing height with a rate.
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