The cheerleaders at a football game launched t-shirts into the crowd from the back of a golf cart that is 2 ft off the ground the t-shirts have an upward velocity of 30 ft per second using the function y equals negative 16 t squared plus 30t + 2 which of the following correctly identifies the y intercepts and best explains its meaning

Question

GPT-4o mini · Answer

To analyze the provided function $ y = -16t^2 + 30t + 2 $, we will first identify its y-intercepts by setting $ t = 0 $, because the y-intercept occurs where the function crosses the y-axis (i.e., when $ t = 0 $): $$ y(0) = -16(0)^2 + 30(0) + 2 = 2 $$ This shows that the y-intercept is at the point $ (0, 2) $. ### Meaning of the Y-Intercept: The y-intercept represents the initial height of the t-shirts at the moment they are launched. In this case, when $ t = 0 $ (the time of launch), the height $ y $ of the t-shirts is 2 feet. This indicates that the t-shirts are being launched from a height of 2 feet above the ground (the height of the golf cart). In summary: - The y-intercept is $ (0, 2) $. - Its meaning is that the t-shirts are launched from a height of 2 feet above the ground.