And I'm way out of my league when it comes to graphing transformations. I understand how to get new coordinates from a mapping rule, but I don't understand how one arrives AT the mapping rule. For example:

1/2(y-1)=(x+3)^2 apparently turns into (x, y) -> (x-3, 2y+1)

I'm told it has a vertical stretch of 2, horizontal translation of -3, and vertical translation of 1. I pretty much get those terms--stretch means, well, you stretch it, and translation means where it moves to.

The best I can figure out is that for some reason, your stretch becomes whatever times your multiplyer of x or y makes one, and your translation is the opposite sign of whatever is added to your x or y.

But I'm not sure this is correct, and if it is, I don't understand WHY.

And maybe when I can understand that, I can better answer the next two questions (how can you tell from the equation that the vertex is at (-3, 1) and how can you tell from the equation that the sketching pattern is over 1, up 2 from the vertex, over 2, up 8, and so on?)

We were supposed to have learned this stuff in grade ten, but I missed a lot of time due to illness, and I'm not even positive that they taught much of it at all.

Any help would be very much appreciated. It's not so much the answers I want as an understanding of the concept.

Thanks!

-Shannon