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.