1. ## mirror image problem

find the image of y=x^2+2x+1 in the line y=x-1

i know how to find image of point on line but how to find image of a curve on line is difficult

2. Now the sophisticated way to do this would be using linear algebra. But i'm too lazy, so i'm going to suggest something more elementary, that to me makes sense would work, and if anyone finds a problem with it, they can point it out.

you want to reflect in the line y = x - 1. (This means also that x = y + 1), so make these substitutions:

The curve $y = x^2 + 2x + 1 = (x + 1)^2$ becomes $x - 1 = [(y + 1) + 1]^2$

Now, solve for $y$. And note that this is not a function. You can graph it piece-wise though

3. why have we substituted the values of x and y