Quadratic Functions from Situations Quick Check

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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=−16t2+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

23.01 feet
23.01 feet

1.03 seconds
1.03 seconds

1.22 seconds
1.22 seconds

−1.03 seconds
negative 1.03 seconds
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1 answer

To find the time when the volleyball reaches its maximum height, we need to determine the vertex of the quadratic function \( h = -16t^2 + 33t + 6 \).

For a quadratic function in the form \( h = at^2 + bt + c \), the time at which the maximum height is reached can be found using the formula:

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

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

Calculating the time \( t \):

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

Rounding this, we can say approximately \( 1.03 \) seconds.

Thus, the domain of the ball when it reaches its maximum height is \( 1.03 \) seconds.

The correct response is:

1.03 seconds