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

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.

Explanation:

Answer 2

f(t)=-16(t-1)^2+24

Explanation:

max 24 is at 1 sec

now, consider the equation:

f(t)=-16(t-h)^2+k,

since (h,k) is vertex, where h is the x value (time in this case), and k is y value (height in this case),

we put in 1 for h and 24 for k

now we have f(t)=-16(t-1)^2+24