SOLUTION: Graph the function. How is the graph a translation of f(x) = x²? y = (x –1)² + 3

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Question 671741: Graph the function. How is the graph a translation of f(x) = x²?
y = (x –1)² + 3
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the graph of 

        y = x²  which is this red graph:

graph%28400%2C400%2C-10%2C10%2C-7%2C13%2C+x%5E2%29

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:

graph%28400%2C400%2C-10%2C10%2C-7%2C13%2C+x%5E2%2C%28x-1%29%5E2%29

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:

graph%28400%2C400%2C-10%2C10%2C-7%2C13%2C+15%2C%28x-1%29%5E2%2C+%28x-1%29%5E2%2B3%29

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