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=16t2+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.