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

1.22 seconds
1.22 seconds

−1.03 seconds
negative 1.03 seconds

1.03 seconds
1.03 seconds

23.01 feet

Answer 1

To find the time at which the volleyball reaches its maximum height, we can use the vertex formula for a quadratic function, given by the equation \( h = -16t^2 + 33t + 6 \). The vertex of a parabolic equation in the form \( h(t) = at^2 + bt + c \) occurs at \( t = -\frac{b}{2a} \).

Here, \( a = -16 \) and \( b = 33 \).

Let's calculate the time \( t \):

\[ t = -\frac{b}{2a} = -\frac{33}{2 \times -16} = \frac{33}{32} \approx 1.03 \text{ seconds} \]

So, the volleyball reaches its maximum height at approximately 1.03 seconds.

Therefore, the domain of the ball when it reaches its maximum height is up to about 1.03 seconds. The valid response based on the available options is:

1.03 seconds.