Algebra 2 Graphing Higher Degree Equations
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Not Going Straight
Graphing Higher Degree Equations

 

 When there are exponents in an equation other than 1,

 the graph of the equation will not be a straight line.
 
 Example:

 Y = X2

 The graph of this puppy looks like this:

 

 
 It forms a sort of U shape with the bottom point at X = 0, Y = 0.
 The left side of the line is a mirror image of the right side.
 The line that divides the two sides of the drawing is the Y axis.
 It is called the line of symmetry of the equation.
 
 Something funny happens with this equation.
 If we put in some number for X and get a Y value,
 then put in the same number but with a minus sign,
 you still get the same Y value.
 
 Watch:
X = 3 X = -3
   
Y=  X2 Y=  X2
Y=  (3)2 Y=  (-3)2
Y=  9 Y=  9
 
 When we can put in a number for X with a plus sign or with a minus sign 
 and get the same Y out both times,
 we call the equation even.
 
 Neither the "symmetrical" thing or  the "even" thing are that big a deal,
 but knowing that kind of stuff impresses math people.
 
 OK, now we'll talk about some more important stuff.
 We drew the graph of Y = X 2
 and found that the bottom point was at the point where X = 0 and Y = 0.
 
 We can move or stretch the "U" this equation makes 
 by putting numbers into the equation at special places.
 
 If you want to move the "U" up,
 just add a number at the right end of the equation.
 To move the "U" up 2 units, add a "+2" at the right end of the equation.
 That means we change Y = X 2 to Y = X 2 + 2:
 

 

 
 If you want to move the "U" down, 
 subtract a number at the right side of the equation.
 If you want to move the "U" down 1,
 stick a -1 at the right side of the equation.
 That means we change Y = X 2 to Y = X 2 - 1:
 

 

 
 If we want to make the "U" skinnier,
 put a number greater than 1 next to the "U" (called a coefficient).
 The larger the number, the skinnier the "U."

 

 
 If you want to make the "U" wider,
 put a fraction less than 1 next to the X.
 The smaller the fraction, the wider the "U."

 

 
 If you want to flip the "U" over and make it look like a conehead,
 put a minus sign in front of the X.
 Even though it's flipped over, all the other stuff still works the same way.

 

 
 Now let's move the "U" to the right.
 To do that, SUBTRACT a number from the X like this.
 WATCH CLOSELY ...

 

 OK, OK, 
 I know it looks backwards for a minus three to move the "U" to the RIGHT,
 but it does.
 The reason is that X has to get up to 3 
 before the total inside the parentheses "( )" gets up to zero.
 If that doesn't make sense to you,
 for now you just have to remember that (X - (stuff)) works sort of backwards.
 
 So putting all this stuff together:
 

 

 
 So Y = -4(X + 1) 2 + 2

 

 

   copyright 2005 Bruce Kirkpatrick

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