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

, 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 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 (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 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 (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.

1 answer

The correct interpretation of the y-intercept of the function \( y = -16t^2 + 30t + 2 \) is:

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

This is because at \( t = 0 \) (the time of launch), the equation simplifies to \( y = 2 \), indicating that the T-shirts are indeed launched from a height of 2 feet.