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
         Quadratic function transition 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
Copyright 2004 - 2020, Nabla Ltd.  All rights reserved.