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Find the polynomial p2 (z) = a0 +ajz+ azz? nat interpolates the ponts (0, -1). (2, –1) and (3,2). (a) The aim of interpolation is for the function to pass precisely through the data points. If p2 (z) is to pass precisely through (0, -1). then P2(0) = ao + 0a +0²a2 =-1 a0 = -1 Write down the equations that must be satisfied for p (z) to pass precisely through the other two data points: P2 (2) = ag+ @2 = P2 (3) = ag+ F (b) Solve the linear system in part-(a) for ag. aj and ag Enter the quadratic interpolating polynomial p (2). Use the "Plot link to check that your answer passes through the data points P2) =

Find the polynomial p2 (z) = a0 +ajz+ azz? nat interpolates the ponts (0, -1). (2, –1) and (3,2). (a) The aim of interpolation is for the function to pass precisely through the data points. If p2 (z) is to pass precisely through (0, -1). then P2(0) = ao + 0a +0²a2 =-1 a0 = -1 Write down the equations that must be satisfied for p (z) to pass precisely through the other two data points: P2 (2) = ag+ @2 = P2 (3) = ag+ F (b) Solve the linear system in part-(a) for ag. aj and ag Enter the quadratic interpolating polynomial p (2). Use the "Plot link to check that your answer passes through the data points P2) =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 66E
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Find the polynomial p, (z) = a0 + ajt + az? that interpolates the points (0, -1). (2, -1) and (3,2). (a) The aim of interpolation is for the function to pass precisely through the data points. if p2 (z) is to pass precisely through (0, -1). then P2 (0) = ao + 0a1 +oa2 = -1 => ao=-1. Write down the equations that must be satisfied for po (a) to pass precisely through the other two data points: P2 P2 (2) = ag+ a2 = P2 (3) = a0+ a2 = (b) Solve the linear system in part-(a) for ag. aj and ag Enter the quadratic interpolating polynomial po () Use the "Plot" link to check that your answer passes through the data points P2(2)
Transcribed Image Text:Find the polynomial p, (z) = a0 + ajt + az? that interpolates the points (0, -1). (2, -1) and (3,2). (a) The aim of interpolation is for the function to pass precisely through the data points. if p2 (z) is to pass precisely through (0, -1). then P2 (0) = ao + 0a1 +oa2 = -1 => ao=-1. Write down the equations that must be satisfied for po (a) to pass precisely through the other two data points: P2 P2 (2) = ag+ a2 = P2 (3) = a0+ a2 = (b) Solve the linear system in part-(a) for ag. aj and ag Enter the quadratic interpolating polynomial po () Use the "Plot" link to check that your answer passes through the data points P2(2)
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