# Parabola System of Equations

Pro Problems > Math > Geometry > Analytic Geometry > Parabolas## Parabola System of Equations

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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Problem by Mr. Twitchell

## Solution

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### Cutting the Parabola

A parabola's equation is given by 2ny = x), find the complete equation of the parabola.

^{2}- 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

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