
The
coordinates of translations formulas and the values of the
coefficients of the source quartic function 
The
basic classification criteria diagram for quartic function 
The
graphs and classification criteria diagram for the quartics
types 4/1 to 4/6 
The
zeros and the abscissas of the turning points of the source quartics
types 4/1 to 4/6 






The
coordinates of translations formulas and the values of the
coefficients of the source quartic function 
Thus,
y
= a_{4}x^{4}
+ a_{3}x^{3}
+
a_{2}x^{2}
+
a_{1}x + a_{0}_{
}or_{ }y

y_{0}
=
a_{4}(x

x_{0})^{4}
+
a_{2}(x

x_{0})^{2}
+
a_{1}(x

x_{0}), 


by
setting x_{0}
=
0 and y_{0}
= 0 we get
the source quartic _{ }y
=
a_{4}x^{4}
+
a_{2}x^{2}
+
a_{1}x. 



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


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


The
zeros and the abscissas of the turning points of the source quartics
types 4/1 to 4/6 
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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