First find the minimum point of the graph.

Since absolute value function can not be negative, the minimum point of the

graph is where .

The original function is

Set original function

               (Subtract 2 from each side)

                     (Additive inverse property: )

                              (Additive identity property: )

               (Multiply each side by negative one)

                                    (Product of two same signs is positive)

Next make at table, fill out the table with values for .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ f(x) = - |x |+ 2 \
\ x \	\  f(x) \
\ -2 \	\ 0 \
\ -1 \	\ 1 \
\ 0 \	\ 2 \
\ 1 \	\ 1 \
\ 2 \	\ 0 \

\

First, draw a co-ordinate plane.

Locate the points on co-ordinate plane and draw the graph through these points. 

Observe the graphs, both graphs have same shape and points on are 2 units higher than the points on .

The graph of  is the graph of and translated 3 units up.

 The graph of  is the graph of and translated 3 units up.