Question 86961
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)?
<pre><font size = 3><b>
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)={{{x^2}}}}. 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:

{{{graph(204.167,350,-10,60,-10,110, 0, x^2*(sqrt(x+3.6)/sqrt(x+3.6))*(sqrt(3.5-x)/sqrt(3.5-x))   ) }}} 

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): 

{{{drawing(204.167,350,-10,60,-10,110, locate (40,100, "(50,100)" ),

graph(204.167,350,-10,60,-10,110, 0, x^2*(sqrt(x+3.6)/sqrt(x+3.6))*(sqrt(3.5-x)/sqrt(3.5-x)),(x-50)^2+100)  )}}} 

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</pre>