don steward
mathematics teaching 10 ~ 16

Thursday, 17 February 2011

cubic graph

what are the coordinates of the various points on this cubic graph?

what would the y-value be
when x = -12?
when x = 16?

maybe use a spreadsheet to ascertain the function

David Wells points out that:
IC is a tangent to the curve at point C and BG is a tangent at G

all cubic curves have rotational symmetry about their point of inflection (E)
and the sum of the x-distances from the point of inflection (E) of the any straight line cutting the curve at three points is always zero (for any cubic)

in the case of a tangent, two of the points are coincident

 what is the equation of this cubic?

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