I'm trying to find the values a, b and c that would validate y=ax2+bx+c with the following parameters:- For x=1;y=1- For x=T;y=S

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I&#039;m trying to find the values a, b and c that would validate y=ax2+bx+c with the following parameters:- For x=1;y=1- For x=T;y=S

star04iks7 · Accepted Answer

First of all, you must realise there is no unique solution for a, b, c, since two points don&#039;t define a unique quadratic parabola.But you can find b,c in terms of a.Solve your equation system by subtracting one from the other:a(S2−1)+b(S−1)=T−1(S−1)[a(S+1)+b]=T−1b=T−1S−1−a(S+1)and c=1−a−b=1−a+a(S+1)−T−1S−1=aS−T−1S−1+1So a is a parameter you can vary, which determines the values of b and c.Note that you weren&#039;t clear about which values must all be positive. If it&#039;s supposed to be all of a, b, c, that very much depends on the values of S and T. For example, when S=3,T=5, if you choose a value of a=1, your b will necessarily be negative. But for the same S and T values, a choice of a=0.35 gives positive values for b(=0.6) and c(=0.05).

I'm trying to find the values a, b

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