Question

Given three data points: (x0, f(x0)), (x1, f(x1)), and (x2, f(x2)), prove the expression for the coefficient b2 in the quadratic interpolation is:________

Answer 1

Answer:

attached below is the prove

Step-by-step explanation:

In order to prove the expression for coefficient b$_{2}$ we have to find b$_{0}$ and b$_{1}$

F(x) = $b_{0} + b_{1} ( x - x_{0} ) + b_{2} ( x - x_{0} ) (x - x_{1} )$

i) Determine b$_{0}$

at x = x$_{0}$  

b$_{0}$ = f(x$_{0}$ )

ii) Determine b$_{1}$

at x = $x_{1}$

f ($x_{1}$) = f ($x_{0}$ ) + b$_{1}$ $(x_{1} - x_{0} )$ + 0

$b_{1} = \frac{f(x_{1} )-f(x_{0} )}{(x_{1}-x_{0} ) }$

prove of the expression for the coefficient B2 in the quadratic interpolation

attached below is the detailed prove