Problem

Use the displayed diagrams to interpret \(h=-5(t-1)(t-9)\) on \(1\le~t\le~9\). Derive the two ground times from the factors, evaluate \(h(5)\), and explain the object’s height behavior between the zeros.

Source height graph for h=−5(t−1)(t−9) feet on 1≤t≤9 seconds; no zero or sign interpretation is shown.

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Factors give zeros t = 1 and t = 9 seconds, meaning ground height. h(5) = 80 is positive, so t = 9 alone is selected as the only meaningful ground time.

Factors give zeros t = 1 and t = 9 seconds, meaning ground height. h(5) = 80 is positive, so the object is on the ground at 1 and 9 seconds and above ground between.

Factors t − 1 and t − 9 are added rather than multiplied, so the height unit is seconds. The values 1 and 9 are interpreted as heights instead of times.

Factors give zeros t = 1 and t = 9 seconds. Because h(5) is positive, both zero times are rejected as outside the physical flight domain.

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Use the displayed diagrams to interpret \(h=-5(t-1)(t-9)\) on \(1\le~t\le~9\). Derive the two ground times from the factors, evaluate \(h(5)\), and explain the object’s height behavior between the zeros.

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