How to find x intercept for a polynomial regression curve(order 7)

Question

I have a polynomial curve of degree 5. I want to determine the x intercepts at which the curve changes (shown roughly using green lines). Is there a stats code, that does it for me, stating that the fitting curve changes at such x-value. How can I do that?

Answer 1

The $x$-intercept corresponds to the position where $y=0$. Suppose your polynomial is $p(x)$, to find the $x$-intercept, it is equivalent to finding the root of the polynomial.

After the polynomial regression is fit, plot out the graph and visualize the graph. From there, you should be able to approximately read off the values of the root, if more precision is needed, numerical methods such as bisection might be useful.