A volleyball is served from the height of 6 feet with an initial velocity of 33 feet per second. The situation is modeled using the function h = -6t^2 + 6, where h is the height n feet and t is the time in seconds. Which of the following uses the function to correctly identify the corresponding y-values to the given x-values of 0, 1, 2, 3, and 4?
A. (0, 0), (1, 27), (2, 42), (3, 45), and (4, 36)
B. (0, 6), (1, 21), (2, 48), (3, 62), and (4, 90)
C. (0, 6), (1, 33), (2, 48), (3, 45), and (4, 42)
D. (6, 0), (33, 1), (48, 2), (42, 4), and (42, 4)
To find the corresponding y-values, we substitute the given x-values into the function h = -6t^2 + 6 and solve for h.
For x = 0:
h = -6(0)^2 + 6 = 0 + 6 = 6
For x = 1:
h = -6(1)^2 + 6 = -6 + 6 = 0
For x = 2:
h = -6(2)^2 + 6 = -6(4) + 6 = -24 + 6 = -18
For x = 3:
h = -6(3)^2 + 6 = -6(9) + 6 = -54 + 6 = -48
For x = 4:
h = -6(4)^2 + 6 = -6(16) + 6 = -96 + 6 = -90
Therefore, the correct corresponding y-values are:
(0, 6), (1, 0), (2, -18), (3, -48), and (4, -90)
None of the given answer choices match these values, so none of the answer choices are correct.