Question

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
ℎ
=
−
6
𝑡
2
+
33
𝑡
+
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, 2, 3, and 4?(1 point)
Responses

(0,0)
(
0
,
0
)
, (1,27)
(
1
,
27
)
, (2,42)
(
2
,
42
)
, (3,45)
(
3
,
45
)
, and (4,36)
(
4
,
36
)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 27 right parenthesis , left parenthesis 2 comma 42 right parenthesis , left parenthesis 3 comma 45 right parenthesis , and left parenthesis 4 comma 36 right parenthesis

(0,6)
(
0
,
6
)
, (1,21)
(
1
,
21
)
, (2,48)
(
2
,
48
)
, (3,69)
(
3
,
69
)
, and (4,90)
(
4
,
90
)
left parenthesis 0 comma 6 right parenthesis , left parenthesis 1 comma 21 right parent

Answer 1

To determine the correct coordinate pairs for the function \( h = -6t^2 + 33t + 6 \), we need to evaluate the function at the specified \( t \) values, which are 0, 1, 2, 3, and 4.

Let's calculate the heights \( h \) at these points:

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

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

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

4. **For \( t = 3 \):**
\[
h(3) = -6(3)^2 + 33(3) + 6 = -54 + 99 + 6 = 51
\]

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

Now we summarize the results:
- \( (0, 6) \)
- \( (1, 33) \)
- \( (2, 48) \)
- \( (3, 51) \)
- \( (4, 42) \)

Comparing these results to the provided options, we find:
- The first proposal listed pairs that do not match the calculated heights.
- The second proposal also does not match accurately.

Thus, neither response is correct based on the computed results of the function \( h = -6t^2 + 33t + 6 \) for the given values of \( t \). The correct corresponding pairs based on our calculations would be \( (0, 6), (1, 33), (2, 48), (3, 51), (4, 42) \).