and his graph:

So, what would the graph of this guy look like?

Let's see what the machine would do... First, the input will get squared... Then, that will have 3 added on...

All the outputs -- the y guys -- ended up 3 higher than before.  It's the exact same shape as Standard Parabola Guy... But, it's moved up 3!

 This movement is called a shift -- specifically, a vertical shift.  (Oh yeah, Baby!  We'll be doing horizontal shifts too.  I'll bet you're not going to be able to sleep now because of the massive glee and anticipation.)

So... What do you think this guy will do?

So, how do I graph these when I'm using my old fashioned computer graphics program -- pencil and paper?  Here's what I do:

Your turn:

Graph these and remember to show your work by identifying what's going on -- not by making a "plotting points" table!

Let's sum up what we've got here...

When there's a number hanging off on the end of Standard Parabola Guy...