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

1.03 seconds
1.03 seconds

−1.03 seconds
negative 1.03 seconds

23.01 feet
23.01 feet

1.22 seconds
1.22 seconds
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Answer 1

To find the time at which the volleyball reaches its maximum height, we need to use the formula for the vertex of a parabola represented by the quadratic function \( h = -16t^2 + 33t + 6 \). The vertex is found at \( t = \frac{-b}{2a} \), where \( a \) is the coefficient of \( t^2 \) and \( b \) is the coefficient of \( t \).

In this case:

• \( a = -16 \)
• \( b = 33 \)

Plugging these values into the formula gives us:

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

Therefore, the answer that corresponds to when the volleyball reaches its maximum height is 1.03 seconds.