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 transition formulas
Quartic function transition formulas
Quintic function transition formulas
Sextic function transition 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   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, where
For n = 4,  quartic   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, where
For n = 5,  quintic  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, where
For n = 6,  sextic  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
Pre-calculus contents F