Relate the domain of a quadratic function to its graph and situation.
Decide whether a given input is meaningful for a quadratic model in context
Problem
Assess \(t=-1~\text{second}\) for a context with \(0\le~t\le~4~\text{seconds}\). Compare the candidate with \(\text{both}~\text{bounds}\), state its interval membership, and explain the real-world meaning of the failed lower-bound test.
Big Picture
What this problem is really about
Membership in a bounded contextual domain requires satisfying every inequality, not merely one endpoint test. We’ll compare the proposed input with both bounds, use the interval markers to handle equality, and translate any failed condition into the timing of the real event.
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