The forms cubic curves can take

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While finding a trend in a data series can be quite useful it is perhaps more interesting to use curves
other than lines and more flexible to approximate such series.
A candidate type of curve that comes to mind are cubics.
Mathematically they are also called curves of the third degree because they represent polynomials
of the third degree.
A question that rises immediately is: "why not use quadratic curves (they are of the second degree)".
The answer to that is: quadratic curves are a special case of cubic curves so we lose nothing by
considering cubics only.
Moreover cubics have two extrema: a minimum
**and** a maximum, while quadratic curves have only one:
a maximum **or** a minimum. *Fig. 3* represents such a curve.
It can be considered as a value that has been rising in the past, reached a maximum,
and then fell down onto a minimum, but caught up afterwards to rise again.

*Fig. 3 * A typical cubic with rising trend having a maximum at -1 and a minimum at +1

On the other hand cubics, like straight lines, can be used to represent descending values.
*Fig. 4* represents such a curve. It represents a value that was declining in the past reached a dip, then raised up for a while and after reaching a maximum continued to fall again.

*Fig. 4 * A cubic with falling trend having a minimum at -1 and a maximum at +1