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# Completing the square

#### A free 2 hours long course

This is a two hour long free course on the method of completing the square. #### Prerequisites

High-school maths, mainly arithmetic.

#### Curriculum

This course concentrates on just one topic, completing the square, which is usually introduced in high-school and then comes back in various courses on college or university level.

# Completing the square

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## Get the outline

A detailed list of the lectures can be found in a PDF outline by clicking this panel. ## Get Completing the square on Udemy

This is a free course on Udemy, so click on this panel to take you directly there to register for the course.

## Course Objectives & Outcomes

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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.
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Completing the square in two variables, one at a time, for identifying conic sections: circles, ellipses, parabolas, and hyperbolas.
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Completing the square in three variables, one at a time, for identifying quadric surfaces: spheres, ellipsoids, hyperboloids, double cones, etc.

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Completing the square in one variable for solving quadratic equations with help of the discriminant and the quadratic formula; derivation of the formula.
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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.
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Completing the square in two or three variables for definiteness of 2×2 or 3×3 matrices / corresponding quadratic forms in 2 or 3 variables.