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)

(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

(6,0)
(
6
,
0

Answer 1

To find the correct corresponding y-values (heights) to the given x-values (time) using the function \( h = -6t^2 + 33t + 6 \), let's evaluate the function at \( t = 0, 1, 2, 3, \) and \( 4 \).

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

2. **For \( t = 1 \)**:
\[
h(1) = -6(1)^2 + 33(1) + 6 = -6 + 33 + 6 = 33
\]
So, the point is \( (1, 33) \).

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

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

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

Putting it all together, the corresponding y-values for the x-values \( 0, 1, 2, 3, \) and \( 4 \) are:

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

Thus, the correct set of points is:

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