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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=−6t2+33t+6
, where h is the height in feet and t is the time in seconds.

Use the function to calculate the h(x) values in the table below.

(3 points)
x h(x)
0
2
4

1 answer

To calculate the values of \( h(x) \) using the function \( h(t) = -6t^2 + 33t + 6 \), we will substitute each value of \( t \) (which we are calling \( x \)) into the function.

  1. For \( t = 0 \): \[ h(0) = -6(0^2) + 33(0) + 6 = 0 + 0 + 6 = 6 \]

  2. For \( t = 2 \): \[ h(2) = -6(2^2) + 33(2) + 6 = -6(4) + 66 + 6 = -24 + 66 + 6 = 48 \]

  3. For \( t = 4 \): \[ h(4) = -6(4^2) + 33(4) + 6 = -6(16) + 132 + 6 = -96 + 132 + 6 = 42 \]

Now, we can fill in the table:

| \( x \) | \( h(x) \) | |---------|------------| | 0 | 6 | | 2 | 48 | | 4 | 42 |

Thus, the completed table is:

  • \( h(0) = 6 \)
  • \( h(2) = 48 \)
  • \( h(4) = 42 \)