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\\)

Explanation:

Identify the vertex of the parabola

$$ (h, k) = (1, 24) $$

Write the vertex form of the quadratic function

$$ f(t) = a(t - h)^2 + k $$

$$ f(t) = a(t - 1)^2 + 24 $$

Verify the initial height using the given options

$$ f(0) = -16(0 - 1)^2 + 24 = -16(1) + 24 = 8 $$

Answer:

• (A) \(f(t) = -16(t - 1)^2 + 24\) (Correct answer)
• (B) \(f(t) = -16(t + 1)^2 + 24\)
• (C) \(f(t) = -16(t - 1)^2 - 24\)
• (D) \(f(t) = -16(t + 1)^2 - 24\)