Polynomial of Degree 2 through Given Points

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Homework Help Overview

The problem involves finding a polynomial of degree 2 that passes through three specified points: (1,-1), (2,3), and (3,13). This falls under the subject area of polynomial functions and linear algebra.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss substituting the given points into the polynomial equation to form a system of linear equations. There is also mention of using concepts from linear algebra, such as reduced row echelon form (rref) and homogeneous solutions.

Discussion Status

The discussion includes various approaches to set up the problem, with some participants suggesting methods to solve the resulting equations. There is an indication of attempts to connect the problem to linear algebra concepts, but no consensus has been reached on a specific method.

Contextual Notes

One participant expresses concern about the lack of coverage of this topic in their textbook, which may affect their understanding of the problem. There is also a reference to a specific section of the textbook that may provide relevant information.

frasifrasi
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Linear Algebra Question...

So, the professor assigned this problem even though the book never touches on it whatsoever. I have no clud how to do it, so I would appreciate if anyone can describe the process of demonstrate.

Q. Find the polynomial of degree 2 whose graph goes through points (1,-1), (2,3), and (3,13).

Thank you for the help!
 
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A polynomial of degree 2 is a*x^2+b*x+c=y. Substitute your three points and you get three linear equation in the variables a,b,c. Solve the system.
 
See the section where it talks about AX = 0, and about homogeneous trivial solutions (or non-trivial).
I strongly think that it would have something about this question in that section.
 
Dick, I think you got it...I will try it.

Should I solve for it by making it in rref ?
 
Last edited:

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