The cheerleaders at a football game launch T-shirts into the crowd from the back of a golf cart that is 2 feet off the ground. The T-shirts have an upward velocity of 30 feet per second. Using the function y=−16t2+30t+2

Question

The cheerleaders at a football game launch T-shirts into the crowd from the back of a golf cart that is 2 feet off the ground. The T-shirts have an upward velocity of 30 feet per second. Using the function y=−16t2+30t+2
, which of the following correctly identifies the y-intercept and best explains its meaning?(1 point)
Responses

The y-intercept is at (2,0)
. The shirts are launched at an initial height of 2 feet.
The y -intercept is at  left parenthesis 2 comma 0 right parenthesis . The shirts are launched at an initial height of 2 feet.

The y-intercept is at (0,2)
. The shirt will reach the ground after 2 seconds from being launched.
The y -intercept is at  left parenthesis 0 comma 2 right parenthesis . The shirt will reach the ground after 2 seconds from being launched.

The y-intercept is at (0,0)
. The shirts are launched from the ground.
The y -intercept is at  left parenthesis 0 comma 0 right parenthesis . The shirts are launched from the ground.

The y-intercept is at (0,2)
. The shirts are launched at an initial height of 2 feet.

GPT-4o mini · Answer

The correct response is: **The y-intercept is at (0,2). The shirts are launched at an initial height of 2 feet.** The y-intercept of a function occurs where $ t = 0 $. In this case, when you substitute $ t = 0 $ into the function $ y = -16t^2 + 30t + 2 $, you find: $$ y = -16(0)^2 + 30(0) + 2 = 2 $$ This means that at time $ t = 0 $, the height $ y $ is 2 feet, which is the initial height from which the T-shirts are launched.