i dont understand how to graph this?

Question

 f(x)=(x+1) to the power of 2 -1

Answer 1

 f( X ) = ( x-1) ²  -1  = X² - 2X + 1 - 1 = X² - 2x

 

 f ( X) = 0      X² - 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).

 

                                      

                                        

Answer 2

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)