The values of the coefficients, a2 and a1 of the source quartic function y = a4x4 + a2x2 + a1x
      The basic classification criteria diagram
      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 = 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 criteria diagram for the quartic 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 and classification criteria diagram for the quartics functions 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 functions types 4/1 to 4/6
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 E
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