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:

0<t<19.6
0<t<19.6
0<t<4
0<t<4

Answer 1

h(t) = -4.9t^2 + 19.6t = -4.9t(t − 4), so h = 0 at t = 0 and t = 4. The vertex is at t = 19.6/(2·4.9) = 2 s with h(2) = 19.6 m.

Domain (physical time): 0 ≤ t ≤ 4 seconds.
Range (height): 0 ≤ h ≤ 19.6 meters.