**Ratan finds the equation of the inverse of the Peg Game rule**

The Peg Game- the object of the game is to interchange the red pegs with the black pegs. Rules: 1.) You can move to an open space next to one, or 2.) you can jump, but only one peg of the other color, and 3.) you can't move backwards.

**Ratan found the rule for the
Peg Game to be x(x+2)=y or x ^{2}+2x=y and graphed this function (the
black curve) and x=y (the orange line of symmetry,
and the inverse, by interchanging the x-coordinates with the y-coordinates (the
purple curve).**

**Ratan then solved the inverse equation for y in
terms of x by completing the square, and checked 3 points on the graph below..**.

**Fine work, Ratan!!**