Algebra 2 Intro to 3D Graphing
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Have a Ball
Intro to 3D Graphing

 

 When we had the equation:

 X2 + Y2 = 25

 
 We set up a graph with an X and Y axis
 to draw the equation line on, like this:
 

 

 
 The graph line turned out to be a circle with a radius of 5,
 that is, every point was 5 units from the center of the circle.
 

 

 
 Now what if we had an equation like:
 

 X2 + Y2 + Z2 = 25

 
 Every point is still 5 units from the center,
 but now we have 3 variables.
 To graph this, 
 we would need to set up a graph with three axis.
 Like this:
 

 

 
 Now the X, Y, Z graph looks kind of funny.
 What it is supposed to be is:
 The X axis goes left and right.
 The Z axis goes up and down.
 AND
 The Y axis goes into and out of the page.
 
 It's a 3 dimensional object,
 and you can't build a 3 dimensional object correctly
 on a 2 dimensional graph.
 
 It's kind of like drawing a cube.
 

 

 
 You have to use your imagination a bit.
 
 So what does a 3 dimensional object,
 where all of the points are 5 units from the center,
 look like?
 

 

 
 A BALL!
 
 We could add and subtract values from any of the variables
 to move the ball around.
 This works just like it did 
 when we graphed other things in the last few pages.
 
 In math, we can use as many variables in an equation as we want.
 
 But once we get past 2 or 3,
 graphing gets pretty tough.
 AND
 We usually need special techniques to solve them,
 mostly using computers.
 

   copyright 2005 Bruce Kirkpatrick

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