I was playing around with Desmos Graphing Calculator and found that the two graphs below intersect at (-1,0), (0,-1), (1.618, 1.618), and (-0.618, -0.618). The latter two points are the golden ratio and the negative of the golden ratio plus 1.
- $y = x^2 - 1$
- $x = y^2 - 1$
Why do the graphs intersect at these points?