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. Using the function, which ordered pair represents the vertex?(1 point)
Responses

(2.75,51.375)
left parenthesis 2.75 comma 51.375 right parenthesis

(0,6)
left parenthesis 0 comma 6 right parenthesis

(51.375,2.75)
left parenthesis 51.375 comma 2.75 right parenthesis

(5.676,0)

Answer 1

To find the vertex of the parabola represented by the function \( h = -6t^2 + 33t + 6 \), we can use the formula for the \( t \)-coordinate of the vertex, which is given by

\[
t = -\frac{b}{2a}
\]

In this case, the coefficients are:
- \( a = -6 \)
- \( b = 33 \)

Plugging in the values, we find:

\[
t = -\frac{33}{2 \cdot -6} = -\frac{33}{-12} = \frac{33}{12} = 2.75
\]

Now, to find the \( h \)-coordinate of the vertex, we can substitute \( t = 2.75 \) back into the height function:

\[
h(2.75) = -6(2.75)^2 + 33(2.75) + 6
\]

Calculating \( (2.75)^2 \):

\[
(2.75)^2 = 7.5625
\]

Now substitute:

\[
h(2.75) = -6(7.5625) + 33(2.75) + 6
\]
\[
= -45.375 + 90.75 + 6
\]
\[
= -45.375 + 96.75
\]
\[
= 51.375
\]

Thus, the vertex of the function is \((2.75, 51.375)\).

Therefore, the correct ordered pair representing the vertex is:

**(2.75, 51.375)**.