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There is some math problems that I can't sort out.

The task is that I have N numbers of coordinates (x;y) given that they fit on a parabola and with them, I have to calculate the (ax^2+bx-c) equation of the parabola.

I could only make it with 3 coordinates but can't get any further.

I have these equations for 3 coordinates:

I made a screenshot from MS Excel so it's more understandable

Any tips or ideas?

introvertbustardxd
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    What do you mean by trying to get farther? – rah4927 Aug 16 '17 at 11:23
  • What do you mean by "can't get any further"? – 5xum Aug 16 '17 at 11:24
  • Well, I would like to calculate the equation using more than 3 coordinates. – introvertbustardxd Aug 16 '17 at 11:27
  • @introvertbustardxd For three coordinates, you get three linear equations in three variables - which is solvable. Three points uniquely define a parabola, as one can infer from this. However with four points, you run the risk that one point falls "outside" of the parabola formed by the three other points. – rah4927 Aug 16 '17 at 11:31
  • @rah4927 So there is no way I could use, for instance, 7 coordinates to calculate the equation, even though theoretically they are fitting the parabolic line? – introvertbustardxd Aug 16 '17 at 11:37
  • @introvertbustardxd if you know the seven points fit a parabolic line, randomly pick any three. Now find your required quadratic. – rah4927 Aug 16 '17 at 12:13

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