A cuspidal cubic is a cubic curve defined by an irreducible polynomial and having a cusp .
A standard affine example is the semicubical
parabola
Its only singular point is the origin , where its tangent line is nodal
cubic tangent lines origin (Faber and Hauser
2010, pp. 374-375).
See also Cubic Curve ,
Cusp ,
Nodal Cubic ,
Semicubical
Parabola
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References Faber, E. and Hauser, H. "Today's Menu: Geometry and Resolution of Singular Algebraic Surfaces." Bull. Amer. Math. Soc. 47 ,
373-417, 2010. https://doi.org/10.1090/S0273-0979-10-01295-4 .
Cite this as:
Weisstein, Eric W. "Cuspidal Cubic." From
MathWorld https://mathworld.wolfram.com/CuspidalCubic.html
Subject classifications
, counted twice. In contrast, the nodal
cubic 
has two distinct tangent lines 
at the origin (Faber and Hauser
2010, pp. 374-375).
