Question

The height of a drone above ground is monitored for 10 seconds. The height of the drone when the monitoring begins is 40 feet. For the first 6 seconds, the height of the drone follows a quadratic pattern. The drone reaches is minimum height of 10 feet 4 seconds into monitoring. The drone's height then increases at a steady rate of 20 feet per second for the remainder of the time it is monitored.

Which piecewise function models the height of the drone x seconds after monitoring begins?

(1 point)

f(x)={158(x−4)2+1020xifif0≤x≤66<x≤10


f(x)={154(x−4)2+1020x+2052ifif0≤x≤66<x≤10


f(x)={158(x−4)2+1020x−2052ifif0≤x≤66<x≤10


f(x)={158(x−4)2+1020x+10ifif0≤x≤66<x≤10

Answer 1

f(x) = { (15/8)(x − 4)^2 + 10, 0 ≤ x ≤ 6
20x − 205/2, 6 < x ≤ 10 }

Explanation: quadratic vertex (4,10) gives f(x)=A(x−4)^2+10; f(0)=40 ⇒ 16A+10=40 ⇒ A=15/8. At x=6: f(6)=(15/8)(2^2)+10=35/2, then linear increase 20 ft/s gives f(x)=20(x−6)+35/2 = 20x−205/2. This corresponds to the third choice.