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Given three arbitrary points on a coordinate system, is there a way to derive an equation that forms the single parabola that passes through all three points?

I guess firstly you would have to prove that given three points, only a single parabola passes through all three, but judging by the fact that a single line passes through two points, and a single horizontal line passes through one point, I would say that a single parabola passes through 3 points.

Anyways, setting that proof aside for now, can anyone think of a way you could do this? I was looking into the standard and general form of a parabola but those forms don't account for a slanted axis of symmetry, which would in general be required to plot most parabolas.

-Edit

Alright, it took me a while, but I see what all of you guys are saying now. There are infinite parabolas that can pass through 3 given points; however, only one parabola of the form ax^2 + bx + c. I finally see that this is the case.

I should be able to find what I'm looking for given this information.

I guess firstly you would have to prove that given three points, only a single parabola passes through all three, but judging by the fact that a single line passes through two points, and a single horizontal line passes through one point, I would say that a single parabola passes through 3 points.

Anyways, setting that proof aside for now, can anyone think of a way you could do this? I was looking into the standard and general form of a parabola but those forms don't account for a slanted axis of symmetry, which would in general be required to plot most parabolas.

-Edit

Alright, it took me a while, but I see what all of you guys are saying now. There are infinite parabolas that can pass through 3 given points; however, only one parabola of the form ax^2 + bx + c. I finally see that this is the case.

I should be able to find what I'm looking for given this information.

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