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
, 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

(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)

Answer 1

Evaluate h(t) = −6t^2 + 33t + 6 for each t:

t=0: h = 6 → (0,6)
t=1: h = −6 + 33 + 6 = 33 → (1,33)
t=2: h = −24 + 66 + 6 = 48 → (2,48)
t=3: h = −54 + 99 + 6 = 51 → (3,51)
t=4: h = −96 + 132 + 6 = 42 → (4,42)

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