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

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