Question

A volleyball is served from a height of 6 feet with an initial velocity of 33 feet per second. It 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 calculate h(x) values in the table

Answer 1

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!