#y=x^2 #graph{x^2 [-10, 10, -5, 5]}

Let's first look at the graph #y=x^2#

If you have a graphing calculator then plot this and then go to the table of values.

#y=x^2-5# graph{x^2-5 [-10, 10, -5, 5]}

Now lets look at #y=x^2-5#. To describe the transformation going on we can see that the function can been shifted down (or translated) down #5# units but how exactly do we know this?

Well, graphically speaking we can see this going on if we take the point #(0,0)# from #y=x^2# and see where it's located in the function #y^2-5#. We find that its now at #(0,-5)# so we say that the graph has been translated down #5# units.

Algebraically, if the above is true for the point #(0,0)# then it must be true for all points on the graph #y-x^2#.

Thus, we translate (or shift) down #5# units for every point on the graph #y=x^2# (Note: We are changing the #y# value for each point so #(0,0)# on #y=x^2# is now #(0,-5)# on #y=x^2-5# NOT #(-5,-5).

I hope this explanation proved to be very helpful and good luck! ;)