SOLUTION: Hello, What about if I know some values for x and y and I want the function? Example: I want to build a curve, arc segment; and I know that when: x=1 y=2 x=2 y=1 We could say y

Question 396635: Hello,
What about if I know some values for x and y and I want the function? Example: I want to build a curve, arc segment; and I know that when:
x=1 y=2
x=2 y=1
We could say y = 3-x, but that isn't a curve.
So, how do I get the curve?
Thanks for the attention!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
With only 2 points, you can put a unique straight line thru them.
If it's any type of curve you have to specify what type curve.
eg, if it's a circle and one point is the center, then that's sufficient.
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But if it's 2 points on the circle, then an infinite # of circles can be made to pass thru them.
The same for parabolas, hyperbolas, and all conic sections.
If you have 3 points and the type of conic section, that's sufficient.
If you have 5 points and know that it's a conic section, that's sufficient.
----------------
A general polynomial can be found to pass thru any number of points.
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