Question

The function h(t) = -4.9t² + 19.6t is used to model the height of an object projected in the air where h(t) is the height (in meters) and t is the time (in seconds). What is the domain and range?

Domain:

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Answer 1

h(t) = −4.9t² + 19.6t models height (m) for time t (s).

Domain: times when h(t) ≥ 0. Factor h(t) = −4.9t(t − 4), so roots at t = 0 and t = 4 and the parabola opens downward. Thus 0 ≤ t ≤ 4 (seconds).

Range: maximum at the vertex t = −b/(2a) = 19.6/(9.8) = 2 s. h(2) = 19.6 m. Heights go from 0 up to 19.6, so 0 ≤ h ≤ 19.6 (meters).

Final:
- Domain: [0, 4] (s)
- Range: [0, 19.6] (m)