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 , 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 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) . 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 (2,0) . The shirts are launched at an initial height of 2 feet.
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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 equation gives:
\[ y = -16(0)^2 + 30(0) + 2 = 2 \]
Thus, the y-intercept is (0, 2), which means that when the T-shirts are launched (at time \( t = 0 \)), they are at an initial height of 2 feet off the ground.
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