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

Question

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

(6,0)
(
6
,
0
)
, (33,1)
(
33
,
1
)
, (48,2)
(
48
,
2
)
, (51,3)
(
51
,
3
)
, and (42,4)
(
42
,
4
)
left parenthesis 6 comma 0 right parenthesis , left parenthesis 33 comma 1 right parenthesis , left parenthesis 48 comma 2 right parenthesis , left parenthesis 51 comma 3 right parenthesis , and left parenthesis 42 comma 4 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 parenthesis , left parenthesis 2 comma 48 right parenthesis , left parenthesis 3 comma 69 right parenthesis , and left parenthesis 4 comma 90 right parenthesis

(0,6)
(
0
,
6
)
, (1,33)
(
1
,
33
)
, (2,48)
(
2
,
48
)
, (3,51)
(
3
,
51
)
and (4,42)
(
4
,
42
)
left parenthesis 0 comma 6 right parenthesis , left parenthesis 1 comma 33 right parenthesis , left parenthesis 2 comma 48 right parenthesis , left parenthesis 3 comma 51 right parenthesis and left parenthesis 4 comma 42 right parenthesis

(0,0)
(
0
,
0
)
, (1,27)
(
1
,
27
)
, (2,42)
(
2
,
42
)
, (3,45)
(
3
,
45
)
, and (4,36)

Answer 1

To determine which set of coordinates accurately represents the function \( h = -6t^2 + 33t + 6 \), we need to calculate the height \( h \) for each value of \( t \) (0, 1, 2, 3, and 4).

Let's calculate the heights:

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

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

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

4. For \( t = 3 \): \[ h = -6(3)^2 + 33(3) + 6 = -6(9) + 99 + 6 = -54 + 99 + 6 = 51 \]

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

Now we have the following pairs of \( (t, h) \):

• \( (0, 6) \)
• \( (1, 33) \)
• \( (2, 48) \)
• \( (3, 51) \)
• \( (4, 42) \)

The correct option that uses the function to identify the corresponding \( y \)-values for the given \( x \)-values of \( (0,6), (1,33), (2,48), (3,51), (4,42) \) is:

(0,6), (1,33), (2,48), (3,51), and (4,42)