To determine how long it takes for the volleyball to reach its maximum height from the context given, we need to know that the vertex of a parabola represents the maximum height for a downward facing parabola.
The vertex form of a quadratic equation is often represented as:
\[ f(x) = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola, and \(a\) determines the direction of the parabola (i.e., whether it opens up or down).
In general, if the quadratic function can be expressed in standard form \( f(x) = ax^2 + bx + c \), the x-coordinate of the vertex (which gives us the time at which maximum height is reached for a downward opening parabola) can also be calculated using the formula:
\[ x = -\frac{b}{2a} \]
Without the specific equation given for the height of the volleyball, we can't compute exactly. However, based on the options you've listed (approximately 15 seconds, 2 seconds, 0.85 seconds, and 5 seconds), the most reasonable time for a volleyball to reach its maximum height after being served is typically around 2 to 5 seconds.
Given the nature of typical projectile motion for a volleyball, approximately 2 seconds is a plausible estimate for the maximum height reached immediately after being served at an initial velocity of 26 ft/sec.
Thus, the best answer is:
approximately 2 seconds.