Algebra 2 Cubic Equations
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Y = X Cubed and it's Buddies
Cubic Equations

 

 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

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