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I am so confused, please help

Determine the equation of g(x) that results from translating the function f(x)= (x+2)^2 to the right 11 units.
I have the choice of four answers.
1. g(x)=(x-9)^2
2. g(x)=(x+13)^2
3. g(x)=(x+2)^2-11
4. g(x)=(x+2)^2+11
I came up with the answer 4. I am new to these types of problems and not sure if I did it correctly.
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2 Answers

Hi Katie!
If you start with f(x) = (x+2)2, that's a parabola w/ vertex at (-2, 0).  If you move the graph 11 units to the right, the vertex will move to the point (9, 0).  But that means the equation of the new graph is g(x) = (x-9)2.  So the answer is actually 1.
Another way to get this is to replace the x in (x+2)2 with x-11... (x-11 + 2)2 --> (x-9)2.  The reason it has to be x-11 instead of x+11 has to do with the fact that because you're shifting the graph to the right 11 units, all the x-values are getting 11 units larger for the same y-values.  Thus, you have to minus 11 to get back the same x-values that corresponded with the y-values you started with.  Hopefully that made a third of sense, it's kind of a retribution thing ("you've increased all my x-values, now I've gotta take them away so the y-values don't notice").  Who says math isn't full of drama?? ;)


Hi Murtaza;
You are correct.
SORRY KATIE!!!!!!!!!!
Hi Vivian,
No worries!  Also, Katie, I wanna say that I recommend graphing the original f(x) AND all four of the answer choices, as I think doing so will help build intuition for these kinds of things.  Each one of those answer choices represents a shift of the original graph 11 units in each of the four cardinal directions, as you'll see.  Study them, arm yourself with the graphing experience!
Hi Katie;
f(x)= (x+2)2
TO THE RIGHT means x+11
We will move 11 positive spaces on the x-axis.
(UP would be y+11).


I really like the way you showed me step by step and explained it clearly. I tried some other problems like this and got them right. Thank you so much!!!!!!

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