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:
- Approximately 0.85 seconds
- Approximately 2 seconds
- Approximately 15 seconds
- 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.