Thread: 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

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.

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 . Why minus one? Think about it like this. To shift it to the right by one means that the value of (what I'll call shifted to the right by one) at a point should be the value assumed one to the left, in other words . Make sense?

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.