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    Analysing a parabola

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    1. 20x=y^2

    2. (x-3)^2 =1/2(y+1)

    3. y2+14y+4x+45=0

    Find the vertex, focus, and directrix of the parabola described by the above equations.

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    https://brainmass.com/math/calculus-and-analysis/analysing-parabola-6785

    Solution Preview

    Standard forms of the parabola are
    y = x^2/4P parabola opens up
    y = -x^2/4P parabola opens down
    x = y^2/4p parabola opens right and
    x^2= -y^2/4p shows a parabola opens left

    For parabolas opening up/down, the directrix is a horizontal line in the form y = + p
    For parabolas opening right/left, the directrix is a vertical line in the form x = + p
    The vertex point for all of the above is (0,0)

    For parabolas opening up/down, the directrix is a horizontal line in the form y = + p. ...

    Solution Summary

    The problem is solved giving all necessary mathematical steps. It will enable you to do similar problems yourself.

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