
The
graphs of the
quartic functions 
The
basic classification diagram for the quartic function 
The
graphs of the quartic function
types 4/1 . . . 6 






The
basic classification diagram for the quartic polynomial function 
By
setting the coefficients a_{2}
and a_{1}
of the source quartic to zero, interchangeably, obtained is the
basic classification shown in the diagram. 

There are
ten types (shapes of the graphs) of quartic functions. 

The
graphs of the quartic function
types 4/1 . . . 6 
Remaining
six types of quartic polynomial satisfy the criteria shown in the
diagram below. 


The
roots of the source quartic
y
=
a_{4}x^{4}
+
a_{2}x^{2}
+
a_{1}x
Types,
4/1, 4/2, 4/3 and 4/4 

the
roots of the Types,
4/5 and 4/6 


The
abscissa of the turning point of the Types,
4/1, 4/2 and 4/3 

the
abscissas of the turning points of the Types, 4/4,
4/5 and 4/6 


The
abscissas of the points of inflection of the
source quartic of Types 4/2
to 4/6, 


The
roots of the translated quartic Type 4
we get by adding x_{0}
to the solutions of the equation 
a_{4}x^{4}
+
a_{2}x^{2}
+
a_{1}x
+
y_{0}
= 0. 













Functions
contents C 



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