Please don't copy in this problem, you are asked to find the best-fit quadraticy = q(x) = ar? + br +cthrough 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= -10For the second step, determine the coefficient matrix A of this system of linear equations.4-21-11A=81-9369-In order to find the "solution" to this system, compute A'A and A'b where b is the column vector of y coordinates.7874-954122A'A=-954122-18122-1841032-10416A'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):a122184Finally, write down the equation of the best-fit quadratic:y = 4 r+-18 2 +122

Given: General quadratic equation is y=qx=ax2+bx+c The equation is passing through the points -2,2,…

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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.3: Parallel And Perpendicular Lines

Problem 32PPS

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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

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