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 (0,0)

. 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 (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.

Answer 1

To analyze the given function \( y = -16t^2 + 30t + 2 \), we identify the y-intercept by evaluating the function at \( t = 0 \):

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

So the y-intercept of the function is \( (0, 2) \).

Now, to interpret this:

• The y-coordinate (2) represents the height of the T-shirts at the moment they are launched, which is from the golf cart that is 2 feet off the ground.

Based on this analysis, the correct response is:

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