Mathematics: Completing the square
Mathematics from high school to university
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2 hours
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Apr 2025
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FREE
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What you will learn
Completing the square: how it is done and why the method works (variants for 1, 2, and 3 variables); a geometric illustration of the method and its name.
Completing the square in one variable for solving quadratic equations with help of the discriminant and the quadratic formula; derivation of the formula.
Completing the square in one variable for plotting polynomials of second degree with help of graph transformations of the parabola y=x^2; finding new vertex.
Completing the square in two variables, one at a time, for identifying conic sections: circles, ellipses, parabolas, and hyperbolas.
Completing the square in three variables, one at a time, for identifying quadric surfaces: spheres, ellipsoids, hyperboloids, double cones, etc.
Completing the square in two or three variables for definiteness of 2x2 or 3x3 matrices / corresponding quadratic forms in 2 or 3 variables.
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4531610
udemy ID
03/02/2022
course created date
26/02/2022
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