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=−16t^2+30t+2

Question

, which of the following correctly identifies the y-intercept and best explains its meaning?(1 point)
Responses

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

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 (0,0)
. 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.

Answer 1

To identify the y-intercept of the function \( y = -16t^2 + 30t + 2 \), we set \( t = 0 \):

\[ y(0) = -16(0)^2 + 30(0) + 2 = 2 \]

This means the y-intercept is at \( (0, 2) \).

The y-intercept represents the initial height of the object when \( t = 0 \), which in this context is the height at which the T-shirts are launched from the golf cart. Since the golf cart is 2 feet off the ground, this indicates that the T-shirts are launched at an initial height of 2 feet.

Therefore, the correct response is:

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