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

1. ## 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

2. 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.

3. Originally Posted by angypangy
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?

4. Originally Posted by angypangy
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.