How can graph of f=-(x-1)^2+6 be obtained from y=x^2?

[cassiemike2000]

I am taking an online finite math class and I am not getting this stuff.

How can the graph of f(x)= -(x-1)^2 +6 be obtained from the graph of y=x^2?

I don't understand how to do this and the book is no help.

Can someone please explain this to me and is there any other substition books that I can get that will help explain this stuff?

Thanks,
Cassie

[stapel_eliz]

Can someone please explain this to me...?

To learn how to do function transformations and translations, try here.

Then note that, for g(x) = x², the function f(x) = -(x - 1)² + 6 is -g(x - 1) + 6....