The translated cubic function
          Graphs of the source and translated cubic functions
The translated cubic function
The general cubic function   y = a3x3 + a2x2 + a1x + a0    or     y - y0 = a3(x - x0)3 + a1(x - x0),
by setting  x0 = 0  and  y0 = 0 we get the source cubic function  y = a3x3 + a1x  where  a1= tan at .
Graphs of the source and translated cubic functions
type 1 y = a3x3 + a2x2 + a1x + a0       or      y - y0 = a3(x - x0)3- x0)3   where,
The root   The point of inflection  I (x0, y0).
type 2/1 y = a3x3 + a2x2 + a1x + a0     or    y - y0 = a3(x - x0)3 + a1(x - x0),    a3  a1 > 0,
  I (x0, y0).
 
type 2/2 y = a3x3 + a2x2 + a1x + a0     or    y - y0 = a3(x - x0)3 + a1(x - x0),    a3  a1 < 0,
If  | y0 | > | yT | | | |
if  | y0 | < | yT |
The turning points The point of inflection  I (x0, y0).
The graphs of the translated cubic functions are symmetric about its point of inflection.
Pre-calculus contents D
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