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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!!!!!!
With all due respect, you are wrong about your answer. The answer is 1. The formula is set up where the negative sign is stationary so when you move right, it has to be negative so then two negatives equal a positive. So with a positive 2 there, you move it 11 units to the right by subtracting it giving you (x-9)^2. I promise.