Use the image to answer the question.

An open, downward facing parabola is graphed on a coordinate plane. The x-axis ranges from negative 2 to 5 in increments of 1. The y-axis ranges from negative 1 to 16 in increments of 2.

Interpret the following quadratic function model and graph given the following context. A volleyball is served into the air at 26 ft./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)
Responses

approximately 0.85 seconds
approximately 0.85 seconds

approximately 2 seconds
approximately 2 seconds

approximately 15 seconds
approximately 15 seconds

approximately 5 seconds
approximately 5 seconds
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1 answer

To determine how long it takes for the volleyball to reach its maximum height, we need to analyze the quadratic function that represents its height over time. In the context of a downward-facing parabola, the maximum height occurs at the vertex of the parabola.

In general, the vertex of a parabola given by the standard quadratic equation \( f(x) = ax^2 + bx + c \) can be found using the formula \( x = -\frac{b}{2a} \). However, if we don't have the specific equation, we can infer the maximum height visually from the graph.

Based on the information provided about the graph’s range and the context of the volleyball’s path, since the curve is downward-facing and is defined on a limited domain (x-axis from -2 to 5), we would typically look for the point on the graph where the height (f(x)) reaches its peak.

Given the options presented:

  1. Approximately 0.85 seconds
  2. Approximately 2 seconds
  3. Approximately 15 seconds
  4. Approximately 5 seconds

Without the specific graph at hand, but knowing that volleyball trajectories typically peak shortly after being served, the most reasonable estimate, based on typical exercises and given choices, would probably be around approximately 2 seconds.

Thus, the answer is:

approximately 2 seconds.