The polynomial functions
       The quartic function
          The source or original quartic function
          The quartic functions classification diagram
       The graphs of the quartic functions types 3/1 and 3/2
Quartic function    y = a4x4 + a3x3 + a2x2 + a1x + a0
Thus,      y = a4x4 + a3x3 + a2x2 + a1x + a0    or    y - y0 = a4(x - x0)4 + a2(x - x0)2 + a1(x - x0),
by setting  x0 = 0  and  y0 = 0 we get the source quartic   y = a4x4 + a2x2 + a1x.
By setting the coefficients a2 and a1 of the source quartic to zero interchangeably, obtained is the basic classification shown in the diagram.
The graphs of the quartic functions types 3/1 and 3/2
type 3 y = a4x4 + a3x3 + a2x2 + a1x + a0    or    y - y0 = a4(x - x0)4 + a2(x - x0)2a1 = 0.
type 3/1 a4a2 > 0
type 3/2 a4a2 < 0
type 3/1
a4a2 > 0
T (x0, y0).
type 3/2
a4a2 < 0
 
Calculus contents A
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