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Quadratic equations and matrices

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Wize University Linear Algebra Textbook > Systems of Linear Equations (SLEs) (Linear Systems)

Polynomial Interpolation

3 Activities

Find a quadratic equation (of the form ax2+bx+c=0ax^2+bx+c=0) that passes through the points (0,-3), (1,-1) and (2,3).

More Polynomial Interpolation Questions:
Find an interpolating polynomial of degree at most 2 of the data points (1,2)\left(1,2\right), (2,0)\left(2,0\right), and (3,12)\left(3,12\right).
Applications
Example: Polynomial Interpolation
Find an interpolating polynomial for the points A(1,1),  B(2,2),  C(0,−2)A(1,1),\ \ B(2,2),\ \ C(0,-2).
Find an interpolating polynomial of degree at most 2 of the data points (0,2)\left(0,2\right), (1,−1)\left(1,-1\right), and (2,1)\left(2,1\right).
Polynomial of least degree
Find the interpolating polynomial of least degree for the data points (0,−3)\left(0,-3\right), (1,−1)\left(1,-1\right), and (−2,5)\left(-2,5\right).
Practice Question: Least Squares for Polynomials
Find the cubic polynomial which best fits the data points (−2,−1),(−1,1),(0,0),(1,−2),(2,3)(-2,-1),(-1,1),(0,0),(1,-2),(2,3) in the least squares sense.
Example: Least Squares for Linear Functions
Example: Least Squares for Linear Functions
Find the equation of the line that comes as close as possible to passing through the points: (0,1),(2,3),(3,4),(4,7)(0,1),(2,3),(3,4),(4,7).
Example: Least Squares for Linear Functions
Example: Least Squares for Linear Functions
Find the equation of the line that comes as close as possible, in the least squares sense, to passing through the points: (0,1),(2,3),(3,4),(4,7)(0,1),(2,3),(3,4),(4,7) .
Solution:
Example: Least Squares for Polynomials
Example: Least Squares for Polynomials
Find the equation of a quadratic polynomial that comes as close as possible to passing through the points: (1,2),(1,3),(2,3)(1,2),(1,3),(2,3).