A volleyball is served by a 6-foot player at an initial upward velocity of 33 feet per second. The situation is modeled by the equation h=−16t2+33t+6

Question

ℎ
=
−
16
𝑡
2
+
33
𝑡
+
6
h representing the height in feet and t representing the time in seconds. Using this equation, define the domain of the ball when it reaches its maximum height.(1 point)
Responses

23.01 feet
23.01 feet

1.22 seconds
1.22 seconds

1.03 seconds
1.03 seconds

−1.03 seconds

Answer 1

To find the time at which the volleyball reaches its maximum height, we can utilize the vertex formula for a quadratic equation of the form \( h(t) = at^2 + bt + c \). The formula for finding the time \( t \) at which the maximum or minimum value occurs is given by:

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

In the given equation \( h(t) = -16t^2 + 33t + 6 \):

• \( a = -16 \)
• \( b = 33 \)

Now, we will calculate \( t \):

\[ t = -\frac{33}{2 \times -16} = \frac{33}{32} \approx 1.03125 \text{ seconds} \]

Thus, the volleyball reaches its maximum height approximately at \( t \approx 1.03 \) seconds.

Since you are asked for the domain of the ball when it reaches its maximum height, it means at the time of maximum height, the height can be considered as maximum.

Among the options you provided, the correct response would be:

1.03 seconds