Algebra 2 Graphing Third Degree Equations
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Just Graph It
Graphing Third Degree Equations

 

 So on the last page we had the equation:

 

 Y = 2X3 - 3X2 - 2X + 3

 
 We figured out that the graph of this 
 crossed the X axis when ...

 

 
 Since the biggest exponent is a 3 and the number next to it is positive
 the graph of this equation looks something like the graph of Y = X 3.

 

 
 The important thing is that the line goes up on the far right side,
 and the line goes down on the far left side.
 Like the graph of Y = X 3 does.
 
 So the graph goes up out to the right and down out to the left.
 We also know that Y = 0 when X = -1  and X = 1 and X = 3/2.
 We can draw in some pieces of the graph from this info ...

 

 Now just connect all of the lines and dots ...
 

 

 
 And that gets us very close to the real graph.
 
 We could get even closer by figuring out a couple more points.
 Like say where X = 0 (always a good one),
 and where X = 1.25.

 

 
 WARNING! WARNING! DANGER! DANGER!
 Even though I drew those last two points 
 as places the graph turns around,
 they might not be the exact places.
 
 The best way to figure out where those places are
 is with some Calculus.
 (Hey! It's something to look forward to!)
 

   copyright 2005 Bruce Kirkpatrick

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