# Intersection between two functions?

How do I find the intersection between $f(x) = 3(x-2)^2$ and $g(x) = 3\sin(x-4)$? It's a sinusodial function so it I couldn't solve it like a normal intersection.

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Are you looking for $x$ such that $f(x) = g(x)$? – user20266 Jun 15 '12 at 16:36
Yes. I would assume to find two $x$s though because it's a quadratic. – user26649 Jun 15 '12 at 16:39
you should then maybe ask for the intersection of the graphs of two functions. To make even clearer what your question is about you could write somthing like 'Intersection of graph of polynomial and sine function' – user20266 Jun 15 '12 at 16:45

## 1 Answer

This leads to a transcendental equation. Typically, you can find approximate solutions for these using numerical root-finding algorithms, like Newton's method or Bisection method.

Typically, an anlytical solution to these could be expressed using special functions, but they don't have nice closed form.

However, in your case, it is easy to prove that, in fact, no solutions exists at all in the real numbers (there are complex ones, though) -- since f(x) is always above g(x).

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