Question

he 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:

mc001-1.jpg

mc001-2.jpg

mc001-3.jpg

mc001-4.jpg

Answer 1

h(t) = -4.9t^2 + 19.6t has roots at t = 0 and t = 4 (factor: -4.9t(t−4)), so physically the object is in the air for 0 ≤ t ≤ 4 seconds. The vertex is at t = 19.6/(2·4.9) = 2 s, giving a maximum height h(2) = 19.6 m.

Domain: [0, 4] (seconds)
Range: [0, 19.6] (meters)