Question

Please help, need answer fast!

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

A

Explanation:

f(t) = –16(t – 1)2 + 24

Answer 2

f(t) = - 16(t - 1)² + 24

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here the vertex = (1, 24)

y = a(t - 1)² + 24

to find a substitute the starting point (0, 8) into the equation

8 = a + 24 ⇒ a = 8 - 24 = - 16

f(t) = - 16(t - 1 )² + 24