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. Using the function, which ordered pair represents the vertex?(1 point)
Responses
(0,6)
left parenthesis 0 comma 6 right parenthesis
(5.676,0)
left parenthesis 5.676 comma 0 right parenthesis
(51.375,2.75)
left parenthesis 51.375 comma 2.75 right parenthesis
(2.75,51.375)
To find the vertex of the parabola represented by the function h = -6t^2 + 33t + 6, we need to consider the standard form of a quadratic function, which is:
f(t) = at^2 + bt + c
where the vertex (h, k) can be found using the formula:
h = -b / (2a)
and then substituting h back into the equation to find k.
Given the function h(t) = -6t^2 + 33t + 6, we have a = -6 and b = 33. Now we can find the time coordinate of the vertex:
h = -b / (2a) = -33 / (2 * -6) = -33 / -12 = 33 / 12 = 2.75
Now that we have the time coordinate of the vertex (h), we can find the height coordinate by substituting t with 2.75 back into the original equation:
k = -6(2.75)^2 + 33(2.75) + 6
k = -6(7.5625) + 90.75 + 6
k = -45.375 + 90.75 + 6
k = 45.375 + 6
k = 51.375
Therefore, the ordered pair representing the vertex is (2.75, 51.375).