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Description:

This Demonstration shows the graphs of two symmetric quadratic functions (with respect to the ... axis) of the form ... and ... , where ... and ... are the horizontal and vertical translations of the corresponding parabolas ... and ... , with vertices at the origin. Their complex zeros are identical and marked by red dots located in the complex plane ... , where the ... and ... axes (labeled in red on the graph) coincide with the Cartesian plane ... coordinate ... and ... axes; that is, the ... axis is also the real axis and the ... axis is also the imaginary axis. While any real zeros lie on the ... axis (or real axis), imaginary zeros come in pairs (complex conjugates) and lie on the vertical line ... that runs through the vertices (and foci) of the parabolas. Further, as complex conjugates, the zeros are symmetric with respect to the ... axis (real axis). To see the effects on the graph when ... , click on the checkbox "force ... to equal ... (vertices = zeros)" and move the ... slider.

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      Keywords:

      EUN,LOM,LRE4,work-cmr-id:262225,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/ComplexZerosOfQuadraticFunctions/,ilox,learning resource exchange,LRE metadata application profile,LRE

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