Question

Use a python code to solve

Use Newton interpolation to find the unique polynomial p2(x) of degree 2 or less, that agrees with the following data: p2(0) = 1, p2(2) = 5, p2(4) = 17.

Answer 1

Explanation of the given question and evaluation:

(Python code attached below)

P₂(0)=1

P₂(2)=5

P₂(4)=17

X	Y	Y	2Y
0	1	4
2	5		8
4	17	12

Using Newtons Intepretation formula

r= x-x₀/h

here x₀=0

h=degree=2

therefore r=x/2;

F(x)=Y₀ + rY₀+ r(r-1)/2²Y

F(x)=1+ x/2*4 +(x/2*(x/2-1)/2 )*8

F(x)=1+x+x²

print("Enter X and Y coordinate respectively")
X0=int(input())
Y0=int(input())
X1=int(input())
Y1=int(input())
X2=int(input())
Y2=int(input())
degree=2
deltaY0= Y1-Y0
deltaY1= Y2-Y1

deltasqY=deltaY1-deltaY0
r="x"
rfrac=2

numpt2eq=int(deltaY0/rfrac)

numpt3eq=int(deltasqY/(degree*rfrac*rfrac))

numpt1eq=str(Y0)


result= numpt1eq+"+"+str(numpt2eq-numpt3eq)+r+"+"+str(numpt3eq)+r+"^2"

print("the equation is :",result)