Without graphing, state how is each graph a translation of f(x)=x^2 horizontal/vertical shifts, reflection, width?
1- f(x)= x^2 + 4
2- f(x)= (x+3)^2
3- f(x)= x^2 - 2
4- f(x)= (x-5)^2
5- f(x)= x^2 + 6
6- f(x)= (x+1)^2

Question

Without graphing, state how is each graph a translation of f(x)=x^2 horizontal/vertical shifts, reflection, width? 
1- f(x)= x^2 + 4 
2- f(x)= (x+3)^2
3- f(x)= x^2 - 2
4- f(x)= (x-5)^2
5- f(x)= x^2 + 6
6- f(x)= (x+1)^2

anonymous · Answer

(1) Vertical shift up by 4
(2) Horizontal shift left by 3 (Plus and minus are reversed in horizontal shifts!)
(3) Vertical shift down by 2
(4) Horizontal shift right by 5
(5) Vertical shift up by 6
(6) Horizontal shift left by 1

anonymous · Answer

Great, but I think that I need VS, HS, width, etc.. for all of the equations? or is that not true?

anonymous · Answer

These equations do not have any changes in width or have been reflected. To change width, you multiply the x inside the squared like (2x + 1)^2 for example. To reflect, you multiply by a negative number to get -x^2 for example.

anonymous · Answer

ah alright then, thanks