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Interpret the following quadratic function model and graph given the following context. A volleyball is served into the air at...Question
Interpret the following quadratic function model and graph given the following context. A volleyball is served into the air at 26ft ./sec from a height of 4.5 ft. The quadratic equation represents the height of the ball over time and in seconds. The graph illustrates this path where x represents the time in seconds and f(x) represents the height in feet. Approximately how long does it take for the volleyball to reach maximum height?
(1 point)
approximately 2 seconds
approximately 15 seconds
approximately 5 seconds
approximately 0.85 seconds
♡
(1 point)
approximately 2 seconds
approximately 15 seconds
approximately 5 seconds
approximately 0.85 seconds
♡
Answers
GPT-4o mini
To determine how long it takes for the volleyball to reach its maximum height based on the given quadratic function model, we need to identify the vertex of the quadratic function. The vertex form of a quadratic function is given by:
\[ f(x) = a(x - h)^2 + k \]
where \((h, k)\) is the vertex. Since the vertex represents the maximum height in this context, \(h\) will give us the time (in seconds) when the volleyball reaches its maximum height.
However, you mentioned that the quadratic equation represents the height of the ball over time but did not provide the actual equation. Nonetheless, if the function is in standard form, \(f(x) = ax^2 + bx + c\), the x-coordinate of the vertex can be found using the formula:
\[ h = -\frac{b}{2a} \]
If we assume common properties of volleyball trajectories, based on the context, we can estimate that the time to reach maximum height is likely around 1 to 2 seconds, since volleyballs serve and ascend quickly.
Given your options:
- approximately 2 seconds
- approximately 15 seconds
- approximately 5 seconds
- approximately 0.85 seconds
Since 2 seconds seems to be the most reasonable estimate for the time it takes for the volleyball to reach the maximum height based on common volleyball serving behavior and trajectories, I would select:
**approximately 2 seconds**.
\[ f(x) = a(x - h)^2 + k \]
where \((h, k)\) is the vertex. Since the vertex represents the maximum height in this context, \(h\) will give us the time (in seconds) when the volleyball reaches its maximum height.
However, you mentioned that the quadratic equation represents the height of the ball over time but did not provide the actual equation. Nonetheless, if the function is in standard form, \(f(x) = ax^2 + bx + c\), the x-coordinate of the vertex can be found using the formula:
\[ h = -\frac{b}{2a} \]
If we assume common properties of volleyball trajectories, based on the context, we can estimate that the time to reach maximum height is likely around 1 to 2 seconds, since volleyballs serve and ascend quickly.
Given your options:
- approximately 2 seconds
- approximately 15 seconds
- approximately 5 seconds
- approximately 0.85 seconds
Since 2 seconds seems to be the most reasonable estimate for the time it takes for the volleyball to reach the maximum height based on common volleyball serving behavior and trajectories, I would select:
**approximately 2 seconds**.