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 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

23.01 feet
23.01 feet

1.22 seconds
1.22 seconds

1.03 seconds
1.03 seconds

Answer 1

To find the time at which the volleyball reaches its maximum height, we can use the formula for the vertex of a quadratic equation. The equation you've provided is in the standard form \( h(t) = -16t^2 + 33t + 6 \).

The time \( t \) at which the maximum height occurs can be determined using the vertex formula: \[ t = -\frac{b}{2a} \] where \( a = -16 \) and \( b = 33 \).

Plugging in the values: \[ t = -\frac{33}{2 \times -16} = \frac{33}{32} \approx 1.03125 \text{ seconds} \quad (\text{or approximately } 1.03 \text{ seconds}) \]

Thus, the time when the ball reaches its maximum height is approximately 1.03 seconds.

Therefore, the correct response regarding the domain of the ball when it reaches its maximum height is:

1.03 seconds