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

Question

𝑦
=
−
16
𝑡
2
+
30
𝑡
+
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)
(
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)
(
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 (0,2)
(
0
,
2
)
. The shirt will reach the ground after 2 seconds from being launched.
The y -intercept is at left parenthesis 0

Answer 1

To find the y-intercept of the function \( y = -16t^2 + 30t + 2 \), we need to determine the value of \( y \) when \( t = 0 \).

Substituting \( t = 0 \) into the equation:

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

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

The correct response is:

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

This indicates that at time \( t = 0 \) seconds (the moment the shirts are launched), their height is 2 feet, which corresponds to the height of the golf cart from which they are being launched.