Graphs of transformation ques

Hello, I don't fully understand this transformation. I understand why the graph goes through 2 & -2. However, I don't understand how they got the Y coordinate as -4 . The sketch in part a) is the graph they want translated btw.

Also, in the second picture, they moved the graph over by 2, I thought when translate f(x) + 4 it will only affect the graph vertically and I can see that as it goes through 4. But the graph moves left by 2

Hello, I don't fully understand this transformation. I understand why the graph goes through 2 & -2. However, I don't understand how they got the Y coordinate as -4 . The sketch in part a) is the graph they want translated btw.

Also, in the second picture, they moved the graph over by 2, I thought when translate f(x) + 4 it will only affect the graph vertically and I can see that as it goes through 4. But the graph moves left by 2

@TeeEm
@SeanFM


I slightly get it now.. for part c, I can see that if you expand the brackets for the original equation and add on 4 you'll get $(x-2)^2$

For part b, I'm still unsure why you subtracted 4 teeEM

@TeeEm
@SeanFM


I slightly get it now.. for part c, I can see that if you expand the brackets for the original equation and add on 4 you'll get $(x-2)^2$

For part b, I'm still unsure why you subtracted 4 teeEM

Ah, I see that you had a second image..

Remember that f(x) = x(x-4), so substituting in x+2 whenever there is an x gives (x+2)((x+2)-4).

For these questions you can find the equations of the graphs but I think the idea is to just apply what you know about transformations, and the equations are just to confirm that you've got it right - sometimes you'll just get a graph and some co-ordinates of interest but not the actual equation, so it's better to rely on the first method.