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

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

A

Step-by-step explanation:

f(t) = –16(t – 1)2 + 24

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.