To determine how long it takes for the volleyball to reach its maximum height, we first need to understand the general form of a quadratic function, which has the formula:
\[ f(x) = ax^2 + bx + c \]
In this context, \( f(x) \) represents the height of the volleyball in feet, and \( x \) represents time in seconds.
The maximum height of a parabola (whose graph represents the function) occurs at the vertex. For a quadratic equation in standard form, the x-coordinate of the vertex can be found using the formula:
\[ x = -\frac{b}{2a} \]
Without knowing the specific coefficients \( a \) and \( b \) from the given quadratic equation, we can still make a reasoned estimate based on the provided options.
In this scenario, since the volleyball is served with a vertical initial velocity and from an initial height, we can reasonably assume that the maximum height would occur in the first few seconds after the serve.
From the options provided: A. approximately 2 seconds B. approximately 5 seconds C. approximately 15 seconds D. approximately 0.85 seconds
Given that volleyball serves typically reach their maximum height relatively quickly, the most plausible options would be A (approximately 2 seconds) or D (approximately 0.85 seconds).
Since A is the nearest estimate for how long it would take for the volleyball to reach its maximum height, the best answer appears to be:
A. approximately 2 seconds.
This estimation aligns well with the typical physics of a volleyball serve, where the ball reaches high points in the range of 1 to 3 seconds.
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