Homework Help is Here – Start Your Trial Now!
Math
Algebra
In this problem, you are asked to find the best-fit quadratic y = q(x) = ax + br + c through the points (-2, 2), (-1, 7), (-9, 17), and (-6, -10). For the first step, write down each linear equation that results from substituting the indicated point in for x and y.

In this problem, you are asked to find the best-fit quadratic y = q(x) = ax + br + c through the points (-2, 2), (-1, 7), (-9, 17), and (-6, -10). For the first step, write down each linear equation that results from substituting the indicated point in for x and y.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question

Please don't copy

in this problem, you are asked to find the best-fit quadratic y = q(x) = ar? + br +c through the points (-2, 2), (-1, 7), (-9, 17), and (-6, -10). For the first step, write down each linear equation that results from substituting the indicated point in for x and y. (-2, 2): 4 a+-2 b+c= 2 (-1, 7): 1 a+ -1 b+c= 7 (-9, 17): 81 a+ -9 b+c= 17 (-6, -10): 36 a+ -6 b+c= -10 For the second step, determine the coefficient matrix A of this system of linear equations. 4 -2 1 -1 1 A= 81 -9 36 9- In order to find the "solution" to this system, compute A'A and A'b where b is the column vector of y coordinates. 7874 -954 122 A'A= -954 122 -18 122 -18 4 1032 -104 16 A'A should always be invertible! Solve the system A' A b = A'b by applying (A'A)-1 to A'b (or use row reduction): a 122 18 4 Finally, write down the equation of the best-fit quadratic: y = 4 r+-18 2 + 122
Transcribed Image Text:in this problem, you are asked to find the best-fit quadratic y = q(x) = ar? + br +c through the points (-2, 2), (-1, 7), (-9, 17), and (-6, -10). For the first step, write down each linear equation that results from substituting the indicated point in for x and y. (-2, 2): 4 a+-2 b+c= 2 (-1, 7): 1 a+ -1 b+c= 7 (-9, 17): 81 a+ -9 b+c= 17 (-6, -10): 36 a+ -6 b+c= -10 For the second step, determine the coefficient matrix A of this system of linear equations. 4 -2 1 -1 1 A= 81 -9 36 9- In order to find the "solution" to this system, compute A'A and A'b where b is the column vector of y coordinates. 7874 -954 122 A'A= -954 122 -18 122 -18 4 1032 -104 16 A'A should always be invertible! Solve the system A' A b = A'b by applying (A'A)-1 to A'b (or use row reduction): a 122 18 4 Finally, write down the equation of the best-fit quadratic: y = 4 r+-18 2 + 122
Expert Solution
steps

Step by step

Solved in 7 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS