NOTES:[br][list=1][br][*]The red arc is the 2nd order Bezier curve: p(t)= A + 2(B-A)t + (C-2B+A)t², 0≤t≤1. [br]To find the vertex, focus, and parabola equation: [url]http://www.geogebratube.org/material/show/id/37814[/url][br][br][br][*] To convert this to an equation in x: [br] [math]\;\;\;[/math]Solve [math]{\small x= 2rt + (1-r) t²}\; [/math] for t.[br] [math]\;\;\;[/math]Then [math] {\small y(x) = 1- t(x)².}[/math][br]The conversion can be put off as long as possible. A, B,C, are sufficient to retrieve both the original function and calculate an approximation. [br][br][*]The analysis graphs don't prove the results. However, it should be clear that we only need to establish[br] [math]\;\;\;[/math]Does the parabola arc cross cos(x)?[br] in the neighborhood of a point where they are tangent. [br][/list] [br]________[br]{The zeros of a polynomial}