A volleyball is served from a height of 6 feet with an initial velocity of 33 feet per second. The situation is modeled using the function `h=-6t^{2}+33t+6`, where `h` is the height in feet and `t` is the time in seconds. Use the function to correctly identify the corresponding y-values to the given x-values of 0, 1, 2, 3, and 4.
To find the corresponding y-values for the given x-values, we substitute the x-values into the function and evaluate for y.
For x = 0:
h = -6(0)^2 + 33(0) + 6
h = 0 + 0 + 6
h = 6
So, when x = 0, y = 6.
For x = 1:
h = -6(1)^2 + 33(1) + 6
h = -6(1) + 33 + 6
h = -6 + 33 + 6
h = 33
So, when x = 1, y = 33.
For x = 2:
h = -6(2)^2 + 33(2) + 6
h = -6(4) + 33(2) + 6
h = -24 + 66 + 6
h = 48
So, when x = 2, y = 48.
For x = 3:
h = -6(3)^2 + 33(3) + 6
h = -6(9) + 33(3) + 6
h = -54 + 99 + 6
h = 51
So, when x = 3, y = 51.
For x = 4:
h = -6(4)^2 + 33(4) + 6
h = -6(16) + 33(4) + 6
h = -96 + 132 + 6
h = 42
So, when x = 4, y = 42.
Therefore, the corresponding y-values to the given x-values of 0, 1, 2, 3, and 4 are 6, 33, 48, 51, and 42, respectively.