Question

The function h(t)= -4.87t^2+18.75t 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 are the domain and range of the function h(t)? Round values to the nearest hundredth.

Answer 1

Interpreting t as time ≥ 0, the object is in the air from t = 0 until it hits the ground. Solve h(t)=0:

-4.87t^2 + 18.75t = 0 → t(−4.87t + 18.75) = 0 ⇒ t = 0 or t = 18.75/4.87 ≈ 3.85 s.

The maximum height occurs at the vertex t = −b/(2a) = 18.75/(9.74) ≈ 1.93 s, and
h_max = 351.5625/19.48 ≈ 18.05 m.

So, rounded to the nearest hundredth:
- Domain: [0, 3.85] seconds
- Range: [0, 18.05] meters