Explanation Given: The points are ( 0.072 , 0.203 ) , ( 0.120 , 0.238 ) , ( 0.148 , 0.284 ) . Calculation: The second degree polynomial function be, p ( x ) = a 0 + a 1 x + a 2 x 2 Substituting x = 0.072 , 0.120 , and 0 .148 into p ( x ) and equating the results to the respective y -values produces the system of linear equations in the variables a 0 , a 1 and a 2 as shown below. p ( 0.072 ) = a 0 + a 1 ( 0.072 ) + a 2 ( 0.072 ) 2 = a 0 + 0.072 a 1 + 0.005184 a 2 = 0.203 p ( 0.120 ) = a 0 + a 1 ( 0.12 ) + a 2 ( 0.12 ) 2 = a 0 + 0.12 a 1 + 0.0144 a 2 = 0.238 p ( 0.148 ) = a 0 + a 1 ( 0.148 ) + a 2 ( 0.148 ) 2 = a 0 + 0.148 a 1 + 0.021904 a 2 = 0.284 The augmented matrix is, [ 1 0.072 0.005184 0.203 1 0.12 0.0144 0.238 1 0.148 0.021904 0.284 ] Solving the system by using Gauss elimination with back substitution: − R 1 + R 2 → R 2 , − R 1 + R 3 → R 3 [ 1 0.072 0.005184 0.203 0 0.048 0.009216 0.035 0 0.076 0.01672 0.081 ] 1 0 To determine b) To graph: The polynomial function showing the points ( 0.072 , 0.203 ) , ( 0.120 , 0.238 ) , ( 0.148 , 0.284 ) .

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN: 9781305658004

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 1.3, Problem 11E

To determine

a)

To calculate:

The polynomial function whose graph passes through the points (0.072,0.203),(0.120,0.238),(0.148,0.284).

To determine

b)

To graph:

The polynomial function showing the points (0.072,0.203),(0.120,0.238),(0.148,0.284).

Expert Solution & Answer

Chapter 1 Solutions

Elementary Linear Algebra (MindTap Course List)

Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...

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a) To calculate: The polynomial function whose graph passes through the points ( 0.072 , 0.203 ) , ( 0.120 , 0.238 ) , ( 0.148 , 0.284 ) .

Solution Summary: The author calculates the second degree polynomial function whose graph passes through the points p(x)=0.25437-1.57907x+12.02224

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a)

To calculate:

The polynomial function whose graph passes through the points (0.072,0.203),(0.120,0.238),(0.148,0.284).

b)

To graph:

The polynomial function showing the points (0.072,0.203),(0.120,0.238),(0.148,0.284).

Chapter 1 Solutions

a) To calculate: The polynomial function whose graph passes through the points ( 0.072 , 0.203 ) , ( 0.120 , 0.238 ) , ( 0.148 , 0.284 ) .

Solution Summary: The author calculates the second degree polynomial function whose graph passes through the points p(x)=0.25437-1.57907x+12.02224

Videos

a) To calculate: The polynomial function whose graph passes through the points (0.072,0.203),(0.120,0.238),(0.148,0.284).

b) To graph: The polynomial function showing the points (0.072,0.203),(0.120,0.238),(0.148,0.284).

Chapter 1 Solutions

a)

To calculate:

The polynomial function whose graph passes through the points (0.072,0.203),(0.120,0.238),(0.148,0.284).

b)

To graph:

The polynomial function showing the points (0.072,0.203),(0.120,0.238),(0.148,0.284).