



There
are two big differences between the graph of Y = X
^{2}



and the
graph of Y = X ^{3}. 


Since Y =
X ^{3} has a bigger exponent, 


it is
skinnier than Y = X ^{2}. 


BUT THE
BIG DIFFERENCE IS THAT THE EXPONENT IS AN ODD NUMBER. 


That
means negative values of X stay negative. 


In this
case, the left side of the graph will go down, not up. 








The graph
of Y = X ^{3} is not the mirror image of itself 


from the
left side to the right side. 


But, you
could put a pin at the origin and spin the paper 180 degrees 


and get
the same graph (except for the labels) 








When you
can do this "Pin and spin" trick, 


math
types say that the equation is called "odd." 


This
equation has no line of symmetry like Y = X
^{2} does, 


but so
it's feelings don't get hurt 


we tell
it that it is symmetrical to the origin (0,0) point. 





X
^{3}
equations can be translated and transformed like X
^{2}
equations 





Example: 








If an
equation with an exponent of 3 or greater isn't factored to begin
with, 


you are
probably not going to be able to factor them without a computer to
help.. 


There are
a few, like perfect cubes, that you will be able to factor, 


but most
that you would meet in real life, you won't 





copyright 2005 Bruce Kirkpatrick 
