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Suppose that the point \\(A\\) has coordinates \\((\\var{x1}, \\var{a*x1^2})\\). Then by the symmetry of the graph the point \\(B\\) has coordinates \\((\\var{-1*x1}, \\var{a*x1^2})\\).

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Geometrically, a function is called even if it is symmetric in the veritcal axis. The picture below is an example of an even function because every point \\(A\\) on the curve can be reflected in the vertical axis to produce another point on the curve \\(B\\).

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Here the line from \\(A\\) to the vertical axis is shown as a solid line, and the reflection from the axis to \\(B\\) is shown as a dashed line.

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{graph(a)}

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Algebraicly, a function has this kind of symmetry whenever

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\\(f(-x) \\equiv f(x).\\)

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A graphical introduction to the concept of even functions a symmery

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If the \\(x\\) coordinate of the point \\(A\\) is \\(\\var{x1}\\) then what is the \\(x\\)-coordinate of the point \\(B\\)?

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If the \\(y\\) coordinate of the point \\(A\\) is \\(\\var{a*x1^2}\\) then what is the \\(y\\)-coordinate of the point \\(B\\)?

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