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The general quartic ... can be brought into the reduced form ... by means of the translation ... . If ... , then ... and ... . The ... coordinates of the two points of inflection of ... are ... , where ... . When ... , there are two real points of inflection and hence three real turning points. When ... , both points of inflection are complex and hence there is only one real turning point. Since ... , ... , and ... are directly related to the geometry of the quartic, this Demonstration offers a more intuitive insight regarding how the shape of the curve is related to the coefficients of the reduced form ... .

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      EUN,LOM,LRE4,work-cmr-id:398054,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/ParametersForPlottingAQuartic/,ilox,learning resource exchange,LRE metadata application profile,LRE

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