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) Responses (0,0) , (1,27) , (2,42) , (3,45) , and (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) , (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 (0,6) , (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 (6,0) , (33,1) , (48,2) , (51,3) , and (42,4)

Answer 1

To find the correct corresponding \(y\)-values for the function \(h = -6t^2 + 33t + 6\) at the given \(x\)-values (\(t\)-values), we will calculate \(h\) for \(t = 0, 1, 2, 3, 4\).

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

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

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

Now we have the corresponding \(y\)-values:

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

So the points are:

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

From the options you provided, the correct set of coordinates is: (0, 6), (1, 33), (2, 48), (3, 51), and (4, 42).