[1] It is affine-symmetric with respect to the axis passing through the point B(x

[2] The symmetry occurs along the direction of the tangent [B

[3] Tangents at points D', D'' symmetric along [B

In the case the curve has two flexes (I, J in the picture below), where the second derivative vanishes, then:

[4] The line of flexes [IJ] is parallel to [B

[5] There is a bitangent [C

[6] The line of flexes [IJ] divides the distance of [C

[7] The segments JK, IJ on the line of flexes are in

First the

The conclusions are easily proved by translating the origin at B' and dividing with the highest power coefficient. Then the curve admits the representation of the form g(x) = x

In this representation line y = v*x coincides with [B

Note that condition u < 0, characterizes the existence of two flexes.

In addition, all quartics are affinely equivalent to one of the three

Feeman, T. G. & Marrero O.

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