Polynomial and/or Polynomial Functions and Equations
The general form or translatable form of the polynomial
The coordinates of translations and the coefficients of the source function formulas
Cubic function formulas
Quartic function formulas
Quintic function formulas
Sextic function formulas
The general form or translatable form of the polynomial
The coordinates of translations and the coefficients of the source function formulas
Therefore, every given polynomial written in the general form can be transformed into translatable form by calculating the coordinates of translations x0 and y0 and the coefficients a of its source function.
Thus, for n = 2,  quadratic   y = a2x2 + a1x + a0   or    y - y0 = a2(x - x0)2,  where
by setting  x0 = 0 and  y0 = 0,        y = a2x2    - the source quadratic.
For n = 3,  cubic function  y = a3x3 + a2x2 + a1x + a0   or   y - y0 = a3(x - x0)3 + a1(x - x0),
by setting  x0 = 0 and  y0 = 0,      y = a3x3 + a1x   - the source cubic function, where
For n = 4,  quartic function  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,    y = a4x4 + a2x2 + a1x   - the source quartic function, where
For n = 5,  quintic function   y = a5x5 + a4x4 + a3x3 + a2x2 + a1x + a0
or   y - y0 = a5(x - x0)5 + a3(x - x0)3 + a2(x - x0)2 + a1(x - x0)
by setting  x0 = 0 and  y0 = 0,    y = a5x5 + a3x3 + a2x2 + a1x   - the source quintic function, where
For n = 6,  sextic function  y = a6x6 + a5x5 + a4x4 + a3x3 + a2x2 + a1x + a0
or   y - y0 = a6(x - x0)6 + a4(x - x0)4 + a3(x - x0)3 + a2(x - x0)2 + a1(x - x0)
by setting  x0 = 0 and  y0 = 0,    y = a6x6 + a4x4 + a3x3 + a2x2 + a1x   - the source sextic, where
Functions contents C