Finding the Maximum Height of a Volleyball Modeled by
To determine the maximum height of a volleyball whose height is modeled by the quadratic equation , one must find the coordinates of the parabola's vertex. Because the coefficient is negative, the parabola opens downward and has a maximum value. First, calculate the axis of symmetry to find the time () the volleyball reaches its peak: . This means the volleyball reaches its maximum height at 5.5 seconds. To find the maximum height, substitute back into the equation: . Therefore, the vertex is (5.5, 488), and the maximum height of the volleyball is 488 feet.
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