Example

Finding the Maximum Height of a Toy Rocket Modeled by h=16t2+208th = -16t^2 + 208t

To find the maximum height of a toy rocket shot upward from the ground at a rate of 208 ft/sec, modeled by the quadratic equation h=16t2+208th = -16t^2 + 208t, we can determine the vertex of the corresponding downward-opening parabola. Since the leading coefficient a=16a = -16 is negative, the parabola opens downward, and the vertex represents the maximum value.

First, calculate the time tt at which the maximum height occurs by finding the axis of symmetry: t=b2at = -\frac{b}{2a} t=2082(16)t = -\frac{208}{2(-16)} t=6.5t = 6.5

The rocket reaches its maximum height after 6.5 seconds. Next, evaluate the maximum height by substituting t=6.5t = 6.5 into the equation: h=16(6.5)2+208(6.5)h = -16(6.5)^2 + 208(6.5) h=16(42.25)+1352h = -16(42.25) + 1352 h=676+1352h = -676 + 1352 h=676h = 676

The maximum height of the toy rocket is 676 feet.

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Updated 2026-04-21

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