SOLUTION: I need help with this homework: use transformations on the graph of y=x^2 to graph y=(x+3)-3. I do not understand any of the problems related to this in this in the lecture notes

Question 86032: I need help with this homework: use transformations on the graph of y=x^2 to graph y=(x+3)-3. I do not understand any of the problems related to this in this in the lecture notes.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you want to shift any function, here is the general rule:

where a represents the units shifted horizontally and k represents the units shifted veritcally

note: notice the negative "a". This means if you have it means shift 3 units in the positive direction. If you have it means shift 3 units in the negative direction. So just remember that the negative is telling you to shift in the opposite direction.

Start with the given function
Replace x with to shift the graph 3 units to the left

Here is the graph
graph of the original equation (red) and the shifted equation (green)
Now subtract 3 from the whole equation to shift the graph down 3 units

Here is the graph

graph of the original equation (red) and the shifted equation (green)

So in short, to shift the graph 3 units to the left and shift the graph 3 units down,you simply use this composite function:

where is your new function
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