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Topic: How would you find the parabolas determined by points {-1,2}, {1,-1},
{2,1}?

Replies: 5   Last Post: Jan 6, 2014 7:58 PM

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RGVickson@shaw.ca

Posts: 1,657
Registered: 12/1/07
Re: How would you find the parabolas determined by points {-1,2},
{1,-1}, {2,1}?

Posted: Jan 6, 2014 7:58 PM
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On Sunday, January 5, 2014 7:21:37 PM UTC-8, Hetware wrote:
> Given the three points (-1,2), (1,-1), and (2,1). (a) Find a parabola
>
> passing through the given points having its axis parallel to the x-axis.
>
> (b) Find a parabola passing through the given points having its axis
>
> parallel to the y-axis.
>
>
>
> I set up the equation
>
>
>
> (y-k)^2=4p(x-h)
>
>
>
> and substituted the given ordered pairs and crunched the numbers. It
>
> became (rather) messy, but I arrived at the given solution. I'm
>
> wondering if there is a more efficient approach to the problem.
>
>
>
> Answers:
>
>
>
> 7(y^2)-3y+6x-16=0
>
> 7(x^2)-9x-6y-4=0


Why not use the Lagrange interpolation formula? See
http://en.wikipedia.org/wiki/Lagrange_polynomial .



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