how do i do it to graph this in a calculator x= y^2 + 2y + 1
You can solve for y, but you may not be happy with the results. You should get TWO different pieces. It is not a "function", so it takes a bit more effort.
I'd just turn the calculator. Don't you think your classmates would get a hoot out of it? Maybe your teacher has a sense of humor? It demonstrates a knowledge of reflection across the line x = y. Don't you want to be the first on in your class to claim that knowledge?
Hahaha you were probably told to graph the inverse of $\displaystyle y =x^2 +x +1 $ as TKHunny said.
You can't take the inverse of a quadratic in polynomial form. You have to complete the square and put it into Turning Point form then swap x and y and solve for y.