Question

A volleyball is served from a height of 6 feet with an initial velocity of 31 feet per second. The situation is modeled using the equation h=−16t2+31t+6
, where h is the height in feet and t is 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, and 2?(1 point)
Responses

(0,6), (1,21), (2,4)
(0,6), (1,21), (2,4)

(0,0), (1,27), (2,2)
(0,0), (1,27), (2,2)

(0,6), (1,31), (2,4)
(0,6), (1,31), (2,4)

(6,0), (31,1), (4,2)

Answer 1

To find the correct y-values for the given x-values (0, 1, and 2) using the function \( h = -16t^2 + 31t + 6 \), we can substitute each x-value (time in seconds) into the equation to find the corresponding height (y-value).

1. For \( t = 0 \):
\[
h(0) = -16(0)^2 + 31(0) + 6 = 6
\]

2. For \( t = 1 \):
\[
h(1) = -16(1)^2 + 31(1) + 6 = -16 + 31 + 6 = 21
\]

3. For \( t = 2 \):
\[
h(2) = -16(2)^2 + 31(2) + 6 = -16(4) + 62 + 6 = -64 + 62 + 6 = 4
\]

Now we can compile the results:

- For \( t = 0 \), \( h(0) = 6 \)
- For \( t = 1 \), \( h(1) = 21 \)
- For \( t = 2 \), \( h(2) = 4 \)

Thus, the correct set of points is \( (0, 6), (1, 21), (2, 4) \).

The appropriate response is:
**(0,6), (1,21), (2,4)**.