Translated cubic functions
         Translated cubic function, the type 1 - the tangent line at the point of inflection is horizontal
         Translated cubic function, the type 2/1 - no turning points, the tangent at inflection is a slant line
         Translated cubic function, the type 2/2 - with two turning points, the tangent at inflection is a slant line
Translated cubic functions
type 1 y = a3x3 + a2x2 + a1x + a0     or      y - y0 = a3(x - x0)3- 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).
Pre-calculus contents E
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