Question

The team mascot shoots a rolled T-shirt from a special T-shirt cannon to a section of people in the stands at a basketball game. The T-shirt starts at a height of 8 feet when it leaves the cannon and 1 second later reaches a maximum height of 24 feet before coming back down to a lucky winner.

If the path of the T-shirt is represented by a parabola, which function could be used to represent the height of the T-shirt as a function of time, t, in seconds?

A: f(t) = –16(t – 1)^2 + 24
B: f(t) = –16(t + 1)^2 + 24
C: f(t) = –16(t – 1)^2 – 24
D: f(t) = –16(t + 1)^2 – 24

Answer 1

A

Explanation:

f(t) = –16(t – 1)2 + 24

Answer 2

These are the main data: the T-shirt starts at a height of 8 feet when it leaves the cannon and 1 second later reaches a maximum height of 24 feet


So, f(0) = 8 feet and f(1) = 24 feet
That means, that you can evaluate the functions at t = 0 and t = 1 to see which represents those two points, (0, 8) and (1, 24).A: f(t) = –16(t – 1)^2 + 24 t = 0 => f(0) = - 16 (0 – 1) ^2 + 24 = -16 + 24 = 8 => This is Ok. t =1 => f(1) = - 16 (1 – 1)^2 + 24 = 0 + 24 => This is Ok.
B: f(t) = –16(t + 1)^2 + 24 t = 0 => f(0) = -16 (0 + 1)^2 + 24 = - 16 + 24 = 8 => this is Ok t = 1 => f(1) = -16 (1 + 1)^2 + 24 = -16(4) + 24 = - 64 + 24 = - 40 => Wrong
C: f(t) = –16(t – 1)^2 – 24 t = 0 => f(0) = -16 (0 – 1)^2 - 24 = -16 – 24 = - 40 => Wrong
D: f(t) = –16(t + 1)^2 – 24 t = 0 => f(0) = - 16 (0 + 1)^2 – 24 = -16 – 24 = - 40 => Wrong
With tha we have obtained that the answer is the option A.