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 = −6t^2 + 33t + 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)

Question

Responses

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

(0,6), (1,21), (2,48), (3,69), and (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

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

Answer 1

To identify the correct pairs of \(x\) (time in seconds) and corresponding \(y\) (height in feet) values using the function \(h(t) = -6t^2 + 33t + 6\), we need to evaluate the function for the given values of \(t\) (0, 1, 2, 3, and 4).

Let's calculate each height:

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 can compile the results:

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

From this, we can see that the correct response is: \[ (0,6), (1,33), (2,48), (3,51) \text{ and } (4,42) \]

So the correct choice is: (0,6), (1,33), (2,48), (3,51) and (4,42).