## Equation of a Curve Rotated About a Point

What is the equation of the curve

$y=f(x)$
after rotation about the point
$(a,b)$
?
It is
$2b-y=f(2a-)) \rightarrow y=2b-f(2a-x)$
.
For example
$f(x)=x^2+2x$
when rotated about the point
$(3,2)$
becomes
$y=2 \times 2- ((2 \times 3 -x)^2+2(2 \times 3 -x)=-44+14x-x^2$
.