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Math Help - Best way to shift x^2 -2x -3 to the right by 1

  1. #1
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    Best way to shift x^2 -2x -3 to the right by 1

    If I have y=x^2 then to shift by 1 on x axis I just do this: (x-1)^2

    But due to constant expression I am a bit confused.

    The only way I can see to do this is to factorise and then shift factors 1 to the right.

    Eg factors of x^2 -2x -3 are (x+1)(x-3) to transform by 1 just add one to each factor: ie becomes x(x-4) - then expand out to x^2 -4x.

    Is that the easiest way to do it?

    Just checking I am using the best technique.

    Angus
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  2. #2
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    Its ok, I have worked it out.

    I see it is quite easy to just do (x-a)^2 - 2(x-1) -3

    The constant has no effect on shift on x axis.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by angypangy View Post
    If I have y=x^2 then to shift by 1 on x axis I just do this: (x-1)^2

    But due to constant expression I am a bit confused.

    The only way I can see to do this is to factorise and then shift factors 1 to the right.

    Eg factors of x^2 -2x -3 are (x+1)(x-3) to transform by 1 just add one to each factor: ie becomes x(x-4) - then expand out to x^2 -4x.

    Is that the easiest way to do it?

    Just checking I am using the best technique.

    Angus
    Yes, in general to 'shift it to the right' by one you need to consider f(x-1). Why minus one? Think about it like this. To shift it to the right by one means that the value of g (what I'll call f shifted to the right by one) at a point should be the value f assumed one to the left, in other words g(x)=f(x-1). Make sense?
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  4. #4
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    Quote Originally Posted by angypangy View Post
    If I have y=x^2 then to shift by 1 on x axis I just do this: (x-1)^2

    But due to constant expression I am a bit confused.

    The only way I can see to do this is to factorise and then shift factors 1 to the right.

    Eg factors of x^2 -2x -3 are (x+1)(x-3) to transform by 1 just add one to each factor: ie becomes x(x-4) - then expand out to x^2 -4x.

    Is that the easiest way to do it?

    Just checking I am using the best technique.

    Angus
    f(x) = (x - 1)^2.

    f(x - 1) = ([x-1] - 1)^2 = (x - 2)^2.

    Draw the graphs to see the obviousness of this.
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