Question

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=−16t^2+33t+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

−1.03 seconds

negative 1.03 seconds
1.03 seconds
1.03 seconds
23.01 feet
23.01 feet
1.22 seconds

Answer 1

To determine the domain of the volleyball when it reaches its maximum height, we first need to find the time at which the ball reaches that maximum height, given by the vertex of the quadratic equation \( h = -16t^2 + 33t + 6 \).

The formula for the time \( t \) at which the maximum (vertex) occurs in a quadratic equation \( h = at^2 + bt + c \) is given by:

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

In this case:
- \( a = -16 \)
- \( b = 33 \)

Now, we can substitute these values into the formula:

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

This indicates that the maximum height occurs approximately at \( t = 1.03 \) seconds.

Thus, the domain of the ball when it reaches its maximum height is from 0 seconds (the moment the ball is served) to approximately 1.03 seconds. Therefore, the ball will reach its maximum height at **1.03 seconds**.

So, the correct response is:
- **1.03 seconds**.