Quadratic Functions from Situations Quick Check

Question

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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

23.01 feet
23.01 feet

1.22 seconds
1.22 seconds

−1.03 seconds
negative 1.03 seconds
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Answer 1

To find the time when the volleyball reaches its maximum height, we can use the vertex formula for a quadratic function in the form of \( h = -16t^2 + 33t + 6 \), which is in the standard form \( h = at^2 + bt + c \).

The time \( t \) at which the maximum height occurs for a parabola given by \( h = at^2 + bt + c \) is found using the formula:

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

Here:

• \( a = -16 \)
• \( b = 33 \)

Plugging in these values:

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

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

So, the correct response among the options provided is:

1.03 seconds.