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.

1 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.