Start with the graph of 

        y = x²  which is this red graph:



Replace x by (x-1) getting the graph of

        y = (x-1)², which is the green graph, 
which you see is the red graph shifted RIGHT
by 1 unit:



Now add +3 to the right side getting

        y = (x-1)²+3, which is the blue graph,
which is the green graph shifted 3 units UPWARD:



So we started with the red graph, replaced the x by (x-1) to
shift it RIGHT by 1 unit to get the green graph, and then 
we added +3 to the right side to shift the green graph UP
to get the final blue graph.


Edwin