Use a system of equations to find the quadratic function f(x) = ax2 + bx + c that satisfies the equations. Solve the system using matrices. f(1)= -2, f(2)= -3, f(3)= -6
Use a system of equations to find the quadratic function f(x) = ax2 + bx + c that satisfies the equations. Solve the system using matrices. f(1)= -2, f(2)= -3, f(3)= -6
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter7: Conic Sections And Quadratic Systems
Section7.4: Solving Nonlinear Systems Of Equations
Problem 63E
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Question
Use a system of equations to find the quadratic function
f(x) = ax2 + bx + c
that satisfies the equations. Solve the system using matrices.
f(1)= -2, f(2)= -3, f(3)= -6
Transcribed Image Text:Step 1
The given quadratic function is f(x) = ax2 + bx + c.
It is given that f(1) = -2, f(2) = -3, and f(3)
Substitute x = 1, x = 2, and x = 3 into f(x) = ax2 + bx + c to form the system of linear equations.
= -6.
f(1) = a + b + c = -2
f(2)
= 4a + 2b + C = -3
f(3) = 9a + 3b + c = -6
b + c = -2
4a + 2b + c = -3.
9a + 3b + c = -6
a +
Therefore, the obtained system of equations is
Write the associated augmented matrix for this system.
1 1 1: -2
4 2 1: -3
9 3 1: -6
To obtain the matrix in reduced row-echelon form, apply elementary row operations until every column that
has a leading 1 has zeros in every position above and below its leading 1.
Perform the operations (R2 - 4R1) on R2 and (R3 - 9R1)
(R3 - 9R:)
on R3.
1.
-2
0 -2
|-3
-3 : 5
5
R2 - 4R1
R3 - 9R1
0 -6
: 12
-8
12
Transcribed Image Text:Perform the operation (-R2)
on R2.
1.
1.
1
-2
3
: -5/2
2
-5/2
1
0 -6 -8 :
12
Perform the operation (R3 + 6R2) on R3.
1 1
1:
-2
3
0 1
|-5/2
-5/2
R3 + 6R2 →
0 0 1 :
|-3
-3
Step 3
(R2 -R3)
Perform the operations
R1 - R3) on R1 and
R1 - R3 →
3R3
1 1
0 1
2.
0 0
1
-3
Perform the operation
R1
R2
on R1.
R1 - R2
1.
-1
2
1
-3
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