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

           (Add 15 to 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 |- 15 \
\ x \	\  f(x) \
\ -10 \	\ -25 \
\ -5 \	\ -20 \
\ 0 \	\ -15 \
\ 5 \	\ -20 \
\ 10 \	\ -25 \

\

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 15 units lower than the points on .

The graph of  is the graph of and translated 15 units down.

 The graph of  is the graph of and translated 15 units down.