Help with translation of quadratic graphs

[jonnburton]

Hi All,

I'm new to the forum. I've been trying to brush up on my maths after not having touched the subject for many years.

I came across one difficulty in the book I'm using today, and that concerns translations of graphs.

I understand the general idea behind translations, but was stumped when I came to the following question:

Describe geometrically the transformation that maps the graph of y = x^2 onto the graph of y = x^2 - 4x + 1

(if the second equation had been y = x^2 - 4 + 1, I think I'd be right in saying the translation would be [4 1] (sorry, I'm not sure how to do things like this in latex)).

The answer in the book says the translation in this case is [2 -3] but I simply can't see how this works...

If anyone can tell me how this works, I'd be very grateful.

 

[Deleted member 4993]

Hi All,

I'm new to the forum. I've been trying to brush up on my maths after not having touched the subject for many years.

I came across one difficulty in the book I'm using today, and that concerns translations of graphs.

I understand the general idea behind translations, but was stumped when I came to the following question:

Describe geometrically the transformation that maps the graph of y = x^2 onto the graph of y = x^2 - 4x + 1

(if the second equation had been y = x^2 - 4 + 1, I think I'd be right in saying the translation would be [4 1] (sorry, I'm not sure how to do things like this in latex)).

The answer in the book says the translation in this case is [2 -3] but I simply can't see how this works...

If anyone can tell me how this works, I'd be very grateful.

Use the technique of completing square:

y = x² - 4x + 1 →

y = x² - 4x + 4 - 4 + 1 →

y = (x - 2)² - 3

Do you see the transformation now...

 

[jonnburton]

Many thanks, Subhotosh! Yes, I see the translation now...

I never thought to do that; this is my difficult with maths at the moment: fitting all the pieces together and knowing the appropriate use of each technique. Hopefully it'll come with practice.

Cheers!