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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

, 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

(0,6)
, (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)
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

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

1 answer

To find the correct pairs of \( (x, y) \) values and verify the function \( h(t) = -6t^2 + 33t + 6 \) for \( t = 0, 1, 2, 3, \) and \( 4 \), we will evaluate the function for each of those values of \( t \).

  1. For \( t = 0 \): \[ h(0) = -6(0)^2 + 33(0) + 6 = 6 \] Thus, \( (0, 6) \).

  2. For \( t = 1 \): \[ h(1) = -6(1)^2 + 33(1) + 6 = -6 + 33 + 6 = 33 \] Thus, \( (1, 33) \).

  3. For \( t = 2 \): \[ h(2) = -6(2)^2 + 33(2) + 6 = -24 + 66 + 6 = 48 \] Thus, \( (2, 48) \).

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

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

Based on these calculations, the corresponding pairs are:

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

The correct response is: (0,6), (1,33), (2,48), (3,51), and (4,42).