I took a quiz today on parametric equations, and there was this one problem that I could not figure out. The question asked me to find $y$ in terms of $x$.
$$x = t^2 - t$$ $$y = t - 1$$
The first thing I tried was solving for $t$ in terms of $x$
$$x = t^2 - t$$ $$ x + t = t^2$$ $$t = \sqrt{x+t}$$
The above didn't work.
I then tried solving for t in terms of y, and then plugging that in for $t$
$$t = y + 1$$ $$x = (y+1)^2 - (y+1)$$ $$x = (y+1)(y+1) - y - 1$$ $$x = y^2 + y + y + 1 - y - 1$$ $$x = y^2 + 2y + 1 - y - 1$$ $$x = y^2 + y$$
That is where I get stuck. Would I have to find the inverse of $x = y^2 + y$?
use the quadratic formula to get $$y=-\frac{1}{2}\pm\sqrt{\frac{1}{4}+x}$$