# Finding a quadratic that has solutions to given values

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.

## 1 answer

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) = K_{1}x + K_{2}

A quadratic can hit three points:

f(x) = K_{1}x^{2} + K_{2}x + K_{3}

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).

## 1 comment thread