Example

Finding the Maximum Height of a Volleyball Modeled by h=16t2+176t+4h = -16t^2 + 176t + 4

To determine the maximum height of a volleyball whose height is modeled by the quadratic equation h=16t2+176t+4h = -16t^2 + 176t + 4, one must find the coordinates of the parabola's vertex. Because the coefficient a=16a = -16 is negative, the parabola opens downward and has a maximum value. First, calculate the axis of symmetry to find the time (tt) the volleyball reaches its peak: t=b2a=1762(16)=5.5t = -\frac{b}{2a} = -\frac{176}{2(-16)} = 5.5. This means the volleyball reaches its maximum height at 5.5 seconds. To find the maximum height, substitute t=5.5t = 5.5 back into the equation: h=16(5.5)2+176(5.5)+4=488h = -16(5.5)^2 + 176(5.5) + 4 = 488. Therefore, the vertex is (5.5,488)(5.5, 488), and the maximum height of the volleyball is 488 feet.

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Updated 2026-04-21

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