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?

f(t) = –16(t – 1)2 + 24
f(t) = –16(t + 1)2 + 24
f(t) = –16(t – 1)2 – 24
f(t) = –16(t + 1)2 – 24

Answer 1

f(t) = –16(t – 1)2 + 24

Reason: the vertex is at (t, h) = (1, 24) so the vertex form is a(t − 1)2 + 24. The parabola opens downward (maximum), so a is negative; using the usual gravity factor in ft/s2 gives a = −16. Checking f(0) = −16(−1)2 + 24 = 8 matches the initial height.