Let the quadratic curve passing through the point (-1,0) and touching the line y=x at (1,1) be y=f(x). Then the x -intercept of the normal to the…

Let the quadratic curve passing through the point $\displaystyle (-1,0)$ and touching the line $\displaystyle y=x$ at $\displaystyle (1,1)$ be $\displaystyle y=f(x)$. Then the $\displaystyle x$-intercept of the normal to the curve at the point $\displaystyle (\alpha, \alpha+1)$ in the first quadrant is $\displaystyle \_\_\_\_$.