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Cutting the Parabola

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Cutting the Parabola

A parabola's equation is given by 2ny = x2 - 6x + m.  Segment AB is a horizontal line segment whose endpoints lie on the parabola, and which contains the point (0,14). The segment has length 24. If the parabola also contains the point (0,
11
4
), find the complete equation of the parabola.

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Problem by Mr. Twitchell

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An upward-opening parabola passes through the points (0, 2), (-4, 6) and (12, 14). What is the equation of the parabola?

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