The polynomial functions
The quartic function
The source or original quartic function
The quartic functions classification diagram
The graphs of the quartic functions types 1 and 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.
There are altogether ten types (shapes of the graphs) of quartic functions.
The graphs of the quartic functions types 1 and 2
 type 1 y = a4x4 + a3x3 + a2x2 + a1x + a0    or    y - y0 = a4(x - x0)4,  a2 = 0 and a1 = 0.
 The zeroes or roots:
 type 2 y = a4x4 + a3x3 + a2x2 + a1x + a0    or    y - y0 = a4(x - x0)4 + a1(x - x0),  a2 = 0.
 The zeroes of the source function:
 The zeroes of the translated function we get by adding x0 to the solution of the equation   a4x4 + a1x + y0 = 0.
Calculus contents A