I'm trying to find the values a, b

Jefferson Pacheco

Jefferson Pacheco

Answered question

2022-04-09

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

Answer & Explanation

star04iks7

star04iks7

Beginner2022-04-10Added 14 answers

First of all, you must realise there is no unique solution for a, b, c, since two points don'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(S21)+b(S1)=T1
(S1)[a(S+1)+b]=T1
b=T1S1a(S+1)
and c=1ab=1a+a(S+1)T1S1=aST1S1+1
So a is a parameter you can vary, which determines the values of b and c.
Note that you weren't clear about which values must all be positive. If it'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).

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