To determine how long it takes for the volleyball to reach its maximum height, we need to identify the vertex of the parabola represented by the quadratic function. Since the parabola opens downward, the vertex will give us the time at which the volleyball's height is at its maximum.
In quadratic functions represented in standard form \(f(x) = ax^2 + bx + c\), the x-coordinate of the vertex (which gives the time at maximum height) can be found using the formula:
\[ x = -\frac{b}{2a} \]
However, since exact values of \(a\) and \(b\) are not given in your question, we rely on the graph.
Given your description, if the graph reaches its maximum height around the time indicated on the x-axis, you would visualize the highest point reached by the vertex of the parabola.
Considering the provided options and understanding that a typical volleyball serve follows a parabolic flight path, it is likely that the maximum height occurs relatively early in the motion (within a few seconds).
To narrow it down:
- Approximately 15 seconds is likely too long for a volleyball's flight.
- Approximately 5 seconds might be plausible but generally would be on the longer side.
- Approximately 0.85 seconds and approximately 2 seconds are more realistic.
If the vertex appears to occur around \(x = 0.85\) or \(x = 2\) seconds based on the graph, you would select the option that aligns with your visualization.
Without the actual graph to reference, I would suggest approximately 0.85 seconds as a potential answer since maximum heights for similar scenarios often occur shortly after launch. However, if the graph clearly indicates otherwise (like closer to 2 seconds), reassess based on that visual.
If you have access to the graph, please ensure to confirm the precise position of the vertex for accuracy.