 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 = 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.
The basic classification diagram for the quartic polynomial function
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 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 = a4x4 + a2x2 + a1x  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 x0 to the solutions of the equation a4x4 + a2x2 + a1x + y0 = 0.   Pre-calculus contents D 