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i dont understand how to graph this?

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2 Answers

 f( X ) = ( x-1)  -1  = X2 - 2X + 1 - 1 = X- 2x
 
 f ( X) = 0      X- 2X = X ( X - 2 ) = 0      X = 0   X =2     (0, 0 ) , ( 2, 0)  X intercepts.
 
   ( 0,0 ) is also Y intercept
 
      a X2 + b X + c   if a > 0 , then quadratic is a parabola opens upward, the (minimum value ,  X = -b/2a )
 
     In this case minimum value [ - ( -2)/2 = 1} , Minimum point( 1, -1) ,
    
        with all this information. Parabola ( X2  -2X ( can be graphed).
 
                                      
                                        
I assume you mean f(x)= (x+1)2- 1.   First you should know that this is a parabola(the U looking graph), because it has the square.  When graphing parabolas, it is all about the vertex. I cannot stress that enough,  If you know the vertex, the rest is easy-peasy.
 
In a problem set up like this we call this form, Vertex Form because it basically spells it out for you.  The vertex here is (-1, -1).  Where did we get this?  (-1,   ) this number came from the parentheses.  What number goes in the parentheses for x that will make the parentheses value 0?  (-1+1) = 0, the is where (-1,  ) came from.  (many people think of it as the opposite of the number inside the parentheses)
 
(   , -1) came from the constant number at the end (        )2 - 1 <--------this.
 
So now that we have the vertex, we can make an x y chart, and pick values for x and plug in to find y.
what I tell my students is put your vertex in the middle of the chart and pick 2 values below and 2 values above.
  x    y
-3
-2
-1    -1
 0
 1
 
After plugging the following values in -3, -2, 0 and 1 and create the ordered pairs and graph them.  It should look like the classic U shape but the vertex is located one unit left and one unit down from the origin. 
 
 
One other example:  if f(x) = (x - 4)2 + 7, then the vertex would be (4, 7) and our chart would look like 
 
   x    y
   2  
   3
   4    7
   5
   6
 
Hope this helps, if any of the explanation is unclear, let me know.
 
(P.S. f(x) can be treated as y)
 

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