Question

1. maria launches a model rocket.

time (seconds): 1, 2, 3, 4
height (feet): 80, 128, 144, 128
which equation models the height h as a
function of time t?
a. \\( h = -16t^2 + 80t \\)
b. \\( h = -16(t + 3)^2 + 144 \\)
c. \\( h = -16(t - 6)^2 + 576 \\)
d. \\( h = -16(t - 3)^2 + 144 \\)

Explanation:

Step1: Test Option A

Substitute \( t = 1 \) into \( h=-16t^{2}+80t \): \( h=-16(1)^{2}+80(1)=-16 + 80 = 64
eq80 \). So A is wrong.

Step2: Test Option B

Substitute \( t = 1 \) into \( h=-16(t + 3)^{2}+144 \): \( h=-16(4)^{2}+144=-16\times16 + 144=-256+144=-112
eq80 \). So B is wrong.

Step3: Test Option C

Substitute \( t = 1 \) into \( h=-16(t - 6)^{2}+576 \): \( h=-16(-5)^{2}+576=-16\times25 + 576=-400 + 576 = 176
eq80 \). So C is wrong.

Step4: Test Option D

Substitute \( t = 1 \): \( h=-16(1 - 3)^{2}+144=-16\times(-2)^{2}+144=-16\times4 + 144=-64 + 144 = 80 \).
Substitute \( t = 2 \): \( h=-16(2 - 3)^{2}+144=-16\times(-1)^{2}+144=-16 + 144 = 128 \).
Substitute \( t = 3 \): \( h=-16(3 - 3)^{2}+144=0 + 144 = 144 \).
Substitute \( t = 4 \): \( h=-16(4 - 3)^{2}+144=-16\times1 + 144 = 128 \). All values match.

Answer:

D. \( h=-16(t - 3)^{2}+144 \)