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Topic: geometry help
Replies: 8   Last Post: Apr 26, 2014 11:56 AM

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Narasimham

Posts: 350
Registered: 9/16/06
Re: geometry help
Posted: Apr 23, 2014 8:00 PM
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Let the 4 points be: (0,2), (1,3), (3,3.6), (5,0.2).

y = d + c x + Sqrt [b + a x ] is the equation of downward parabola. By changing sign before radical sign you obtain upward parabola.

Mathematica program is:

y[a_,b_,c_,d_,x_]= Sqrt[a x + b ]+ c x +d
NSolve[{2.-y[a,b,c,d,0]==0, 3.-y[a,b,c,d,1]==0, 3.6 -y[a,b,c,d,3]==0, 0.2-y[a,b,c,d,5] == 0},{a,b,c,d}]

{{a->-355.769,b->2176.17,c->4.98328,d->-44.6495}}

Plot[Sqrt[ -355.76915062347183` x + 2176.1738248547367` ] + 4.983277684410211` x -44.64947829134573` , { x, -1, 6},PlotStyle-> {Red,Thick}, GridLines-> Automatic]

The equation of parabola is a special case of general conics.

HTH
Narasimham



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