SOLUTION: Draw a graph of f(x)=x^2. Use it to properly draw a graph of g(x)=(x-50)^2+100. What must be done to properly graph g(x)?

To go from the right side of f(x) to the right 
side of g(x), we must:

1. Replace x by (x-50)
2. Add 100 to the right side

Step 1 shifts the graph 50 units RIGHT, then
step 2 shifts the graph 100 units UP.

Here's the graph of f(x)=}. It's a little tiny green 
parabola at the origin.  Look carefully and you'll see it. I had 
to draw it tiny because it has to be shifted so much:

 

Now we shift the green graph of f(x) to the blue one 
up at the top right which is the graph of g(x): 

 

Notice that the vertex of the original green graph of 
f(x) is (0,0) and it has shifted to the point (50,100),
the vertex of g(x).

Edwin