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 equation h=−6t2+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

(0,6), (1,21), (2,48). (3,69), and (4,90)
(0,6), (1,21), (2,48). (3,69), and (4,90)

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

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

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

Answer 1

To find the y-values corresponding to the x-values of 0, 1, 2, 3, and 4 using the function \( h(t) = -6t^2 + 33t + 6 \), we need to plug each x-value (time in seconds) into the equation and calculate the 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 summarize the calculated values:

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

Matching these results to the provided options, the correct pair is:

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