Finding the Maximum Height of a Stone Modeled by
To find the maximum height of a stone thrown upward from a height of 32 feet at a rate of 128 ft/sec, modeled by the quadratic equation , we can find the vertex of the corresponding downward-opening parabola. Because the leading coefficient is negative, the parabola opens downward, meaning the vertex represents the maximum value.
First, determine the time at which the maximum height occurs by calculating the axis of symmetry:
The stone reaches its maximum height after 4 seconds. Next, evaluate the maximum height by substituting into the equation:
The maximum height of the stone is 288 feet.
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