how to find parabola function given a few points?

I have a parabola, just need to find the function:

here are few points on the graph i traced

please, don't just give answer, I need to know how to do it. feels like i need the speed graph to figure out the parabola function but have no idea.(Thinking)

or you can give me the function and then tell me how you get it. much much appreciated. thanks in advance

x y

start with

( 0 0)

18 | 16 |

60 | 61 |

101 | 110 |

170 | 207 |

283 | 410 |

344 | 557 |

402 | 740 |

Re: how to find parabola function given a few points?

Use a regression method:

Least Square Method

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Re: how to find parabola function given a few points?

Hi !

Of course, least squares fitting of the parabolic function y = c_{0}*x^{2}+c_{1}*x+c_{2} will give you an approximate of your data.

But I suggest to perform both "absolute least squares" and "relative least squares" fittings. The coefficients c_{0}, c_{1}, c_{2} will be sligthly different. The first leads to a better Absolute Deviation, while the second leads to a better Relative Deviation. So you can chose the best on the physical point of view.

For more information, see the paper "Régressions coniques, quadriques, circulaire, sphérique..." (in French, not translated yet)

http://www.scribd.com/JJacquelin/documents

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Re: how to find parabola function given a few points?

If you want that the point (0,0) be exactly on the parabola, the equation is : y = c_{0}*x^{2} + c_{1}*x

For more information, see the paper "Régressions coniques, quadriques, circulaire, sphérique..." (in French, not translated yet),

through the link : Scribd