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Interpolate f at the points $x-h , x$ and $x+h$ by a quadratic polynomial $p(x)$.

Let $ \ p(x)=a+bx+cx^{2} \ $. Now,\begin{align} p(x-h)=f(x-h)=a+b(x-h)+c(x-h)^{2}, \\p(x)=f(x)=a+bx+cx^{2} , \\ p(x+h)=f(x+h)=a+b(x+h)+c(x+h)^{2}, \end{align}

But now this is tedius to find out the constants $a, b, c$.

Any help please.

Jaideep Khare
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MAS
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  • What do you mean by tedious? You can plug this into a software like mathematica or do the calculations by hand. – Gregory Apr 14 '17 at 20:05
  • I don't have software facility but I want to mean is this the process for quadratic polynomial approximation ? – MAS Apr 14 '17 at 20:07
  • In hand it is being lengthy , please help me with short calculation – MAS Apr 14 '17 at 20:08
  • The calculations are not really short, but the problem is setup correctly, you have three equations and three unknowns since you assume $x,h$ is known. – Gregory Apr 14 '17 at 20:14

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