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)