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)

Question

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 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

Answer 1

The correct response is:

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

Explanation:

In the function \( y = -16t^2 + 30t + 2 \), the y-intercept occurs when \( t = 0 \). Plugging \( t = 0 \) into the function gives us:

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

So, the y-intercept is at the point (0, 2). This indicates that the T-shirts are launched from an initial height of 2 feet, which corresponds to the height of the golf cart.