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Q&A

Finding a quadratic that has solutions to given values

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Hi, i wanted to see if there is an algorithm for finding/approximating a quadratic formula that resulted in (at least one) wanted value

i remember finding a math.stackexchange post long time ago about the quadratic that results in (pi,e), in one of the answers suggested was a method to approximate with a given computer program that searched in a specific range..but i couldn't find it again

anyways any help would be appriciated.

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This one? https://math.stackexchange.com/questions/498393/finding-an-integer-coefficients-quadratic-e... (1 comment)

1 answer

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If you only have one X-Y pair to meet, then a constant fits the specs perfectly:

    f(x) = K

If it has to meet two X-Y pairs, then a line does it:

    f(x) = K1x + K2

A quadratic can hit three points:

    f(x) = K1x2 + K2x + K3

This is also known as a "second order" polynomial. Each additional order allows the function to hit one more point exactly (within some limits, like they all have to have different X values).

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the Lagrange interpolation formula is an explicit formula for the polynomial of degree $n$ matching $... (1 comment)

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