To find the height \( h \) of the volleyball at various time values \( t \), we can use the function provided:
\[ h(t) = -6t^2 + 33t + 6 \]
Let's calculate \( h(t) \) for a few specific time values. Here's a table for \( t = 0, 1, 2, 3, 4, 5 \):
| Time (t in seconds) | Height (h in feet) | |----------------------|---------------------------| | 0 | \( h(0) = -6(0)^2 + 33(0) + 6 = 6 \) | | 1 | \( h(1) = -6(1)^2 + 33(1) + 6 = -6 + 33 + 6 = 33 \) | | 2 | \( h(2) = -6(2)^2 + 33(2) + 6 = -24 + 66 + 6 = 48 \) | | 3 | \( h(3) = -6(3)^2 + 33(3) + 6 = -54 + 99 + 6 = 51 \) | | 4 | \( h(4) = -6(4)^2 + 33(4) + 6 = -96 + 132 + 6 = 42 \) | | 5 | \( h(5) = -6(5)^2 + 33(5) + 6 = -150 + 165 + 6 = 21 \) |
Now, let's summarize these calculations in the table:
| Time (t in seconds) | Height (h in feet) | |----------------------|---------------------| | 0 | 6 | | 1 | 33 | | 2 | 48 | | 3 | 51 | | 4 | 42 | | 5 | 21 |
If you need calculations for additional time values, please let me know!