Equation

Is 4x⁴ + 3x² + 9y + 3 = 0 symmetrical to the x axis, y axis, origin or all three?

To test for y axis symmetry substitute -x in for every x.   If the resulting equation is the same then
it is symmetrical to the y axis:  4(-x)⁴ + 3(-x)² + 9y + 3 = 0   →   4x⁴ + 3x² + 9y + 3   =   0
The results is the same as the original equation and hence the equation is symmetrical to the y axis.   

To test for x axis symmetry substitute -y in for every y:   4x⁴ + 3x² + 9(-y) + 3 = 0   →   4x⁴ + 3x² - 9y + 3 = 0
The results differs from the original equation hence it is not symmetrical to the x axis.

To test for origin symmetry substitute -y in for every y and -x for every x:   4(-x)⁴ + 3(-x)² + 9(-y) + 3 = 0   →   4x⁴ + 3x² - 9y + 3   =   0
The results differs from the original equation hence it is not symmetrical to the origin.


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