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

Algebra ->  Graphs -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
If you want to shift any function, here is the general rule:

f%28x-a%29%2Bk where a represents the units shifted horizontally and k represents the units shifted veritcally

note: notice the negative "a". This means if you have f%28x-3%29 it means shift 3 units in the positive direction. If you have f%28x%2B3%29 it means shift 3 units in the negative direction. So just remember that the negative is telling you to shift in the opposite direction.


f%28x%29=x%5E2 Start with the given function
f%28x%2B3%29=%28x%2B3%29%5E2Replace x with x%2B3 to shift the graph 3 units to the left

Here is the graph
graph of the original equation y=x%5E2 (red) and the shifted equation y=%28x%2B3%29%5E2(green)
f%28x%2B3%29-3=%28x%2B3%29%5E2-3 Now subtract 3 from the whole equation to shift the graph down 3 units

Here is the graph

graph of the original equation y=x%5E2 (red) and the shifted equation y=%28x%2B3%29%5E2-3(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:

g%28x%29=f%28x%2B3%29-3 where g%28x%29 is your new function