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

For this parabola we have:
f ( 0 ) = 8
and : f ( 1 ) = 24
In the first equation ( A) :
f ( 0 ) = - 16 * ( 0 - 1 )² + 24 = - 16 * 1 + 24 = 8 ( correct )
f ( 1 ) = - 16 * ( 1 - 1 )² + 24 = 24  ( correct )
For B:
f ( 0 ) = - 16 * ( 0 + 1 )² + 24 = - 16 + 24    = 8  ( correct )
f ( 1 ) = - 16 * ( 1 + 1 )² + 24 = - 16 * 4 + 24 = - 64 + 24 = 40 ( false )
For C:
f ( 0 ) = - 16 * ( 0 - 1 )² - 24 = - 16 - 24 = - 40 ( false )
f ( 1 ) = - 16 * ( 1 - 1 )² - 24 = - 24  ( false )
For D:
f ( 0 ) = - 16 * ( 0 + 1 )² - 24 = - 16 - 24 = - 40 ( false )
f ( 1 ) = - 16 * ( 1 - 1 )² - 24 = - 24   ( false )
Answer:
A )  f ( t ) =  - 16 * ( t - 1 )² + 24
   

Answer 2

Answer:  f(t) = -16(t - 1)2 + 24

Step-by-step explanation:        

Here f(t) represents the path of the T-shirt in t seconds.

Since, It is given,

Initially, t = 0 and f(t) = 8

And, For t = 1, f(t) = 24

Thus, (0,8) and (1,24) are the points of given parabola.

⇒These points must satisfy the equation of the parabola.

When we put x = 0 and y = 8 in all the equations one by one,

We found, Equations  f(t) = -16(t - 1)2 - 24, f(t) = -16(t + 1)2 - 24 are not satisfying.

Therefore, they can not be the equation of the given parabola.

Again by putting x = 1 and y = 24,

f(t) = -16(t + 1)2 + 24 is not satisfying.

Therefore f(t) = -16(t + 1)2 + 24 also can not be the equation of the given parabola.

Thus, Only equation f(t) = -16(t - 1)2 + 24 is satisfied by the points (0.8) and (1,24).

⇒ f(t) = -16(t - 1)2 + 24 can be the equation of the given path of T-shirt.