4. Determine the function using Interpolation. Show the step-by-step process for each interpolation similar to the solution in the lecture notes. Fit the following data points using Lagrange Interpolating polynomial. Show the simplified expression for each Lagrange term only. Determine the function at x = 5.5 x -2 03 f(x) -34 -2 -6.5 7 15.5

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.6: Solving Quadratic Equations By Using The Quadratic Formula
Problem 64PFA
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4. Determine the function using Interpolation. Show the step-by-step process for
each interpolation similar to the solution in the lecture notes. Fit the following
data points using Lagrange Interpolating polynomial. Show the simplified
expression for each Lagrange term only. Determine the function at x = 5.5
X-2 03
7
f(x) -34 -2 -6.5 15.5
5. Fit the following data points using Newton's Divided Difference Interpolating
polynomial. Show the step-by-step divided difference up to the last forward finite
divided difference. Do not simplify the final function. Determine the function at x
= 9.5
X 0
2
4
6
8
10
12
f(x) 52.698 53.414 49.002 41.718 35.354 35.238 48.234
Transcribed Image Text:4. Determine the function using Interpolation. Show the step-by-step process for each interpolation similar to the solution in the lecture notes. Fit the following data points using Lagrange Interpolating polynomial. Show the simplified expression for each Lagrange term only. Determine the function at x = 5.5 X-2 03 7 f(x) -34 -2 -6.5 15.5 5. Fit the following data points using Newton's Divided Difference Interpolating polynomial. Show the step-by-step divided difference up to the last forward finite divided difference. Do not simplify the final function. Determine the function at x = 9.5 X 0 2 4 6 8 10 12 f(x) 52.698 53.414 49.002 41.718 35.354 35.238 48.234
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