# Math Help - Invariant - fixed point.

1. ## Invariant - fixed point.

question is

the graph $y=(x-2)^{2}-1$ represents y=f(x). What are the coordinates of the points that would be invariant for the transformations?
then it has a list of 5 equations to find these points for.

2. I think you're a little on the wrong track here. A fixed point is one that doesn't change after a transformation. Consider this simple example f(x)=x and the transformation f --> f^2. What points are fixed? In other words what values of x satisfy f(x)=f^2(x). The solution is fairly simple:

$f(x)=f^2(x)$

$x=x^2$

x=0 or x=1.

Now let's look at your problem:

The transformation is f --> -f, so:

$f(x)=-f(x)$

$2f(x)=0$

$f(x)=0$

$(x-2)^2-1=0$