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A frog is sitting on a stump 2 feet above the ground. It hops off the stump and lands...

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hinkberries | Student, Undergraduate | (Level 1) Honors

Posted April 27, 2011 at 8:05 AM via web

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A frog is sitting on a stump 2 feet above the ground. It hops off the stump and lands on the ground 4 feet away. During its leap, its height h is...

given by the equation h= -0.5x^2 + 1.5x + 2 where x is the distance in feet from the base of the stump, and h is the height in feet. How far was the frog from the base of the stump when it was 1.32 feet above the ground? Simplify answer and round to nearest tenth if needed.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 27, 2011 at 11:08 AM (Answer #1)

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The height of the frog is given by the equation h = -0.5x^2 + 1.5x + 2, where x is the distance in feet from the base of the stump in feet.

Let the distance that the frog is from the base of the stump when its height is 1.32 feet be x.

This gives: 1.32 = -0.5x^2 + 1.5x + 2

=> -0.5x^2 + 1.5x + 0.68 = 0

=> 0.5x^2 - 1.5x - 0.68 = 0

=> x^2 - 3x - 1.36 = 0

x = 3/2 + sqrt(9 + 5.44) / 2

=> x = 3/2 + sqrt (14.44)/2

=> x = 1.5 + 1.9

=> x = 3.4 feet

The height of the frog is 1.32 feet when its distance from the base of the stem is 3.4 feet.

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