

The
graphs of the quartic function

The
basic classification diagram for the quartic polynomial 
The
graphs of the quartic function
Types, 4/1 . . . 4/6 





The 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 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. 


The
graphs of the quartic function
Types, 4/1 . . . 4/6 
Remaining
six types 4/1...6 of quartic polynomial functions 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. 












Precalculus contents
D 



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