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How does geogebra quickly determine the analytical formula of a parabola passing through three point
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How does geogebra quickly determine the analytical formula of a parabola passing through three points?For example, a parabola passes through three points: A (2,0), B (4,0), and C (0,2).
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Form polynomial with the 3 points (A,B,C). Then place 2 additional points (D,E) on the function. Then form the conic section with the 5 points (A,B,C,D,E).
Addition:
create the directrix and focus to the Conic . Use these two to create the parabola (yields shortened coefficients)
Finally, a user tool can be created (ggt)
You need to do exactly what you would do on paper, e.g. create a system of 3 equations in 3 variables using the general equation of the parabola (first of all figure out which one it is (x=... or y=...), depending on the position of the three points, then telling to the parabola to pass through A, B and C respectively.
or
Form polynomial with the 3 points (A,B,C). Then place 2 additional points (D,E) on the function. Then form the conic section with the 5 points (A,B,C,D,E).
Addition:
create the directrix and focus to the Conic . Use these two to create the parabola (yields shortened coefficients)
Finally, a user tool can be created (ggt)
http://mathworld.wolfram.co...
What about
FitPoly({A,B,C}, 2)
?
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