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).

Best Answer
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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)

Comments (8)

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1

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.

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1

Thank you, this is general practice.

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2

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)

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1

Thank you。

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1

Thank you

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2

What about

FitPoly({A,B,C}, 2)

?

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1

Thank you。

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