Completing the square

A free 2 hours long course

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

Image precalculus part 1
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Prerequisites

High-school maths, mainly arithmetic.
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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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A detailed list of the lectures can be found in a PDF outline by clicking this panel.

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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.
Justin M.
Udemy student
Due to the great explanations and plenty of examples, I was able to actually understand completing the square instead of just being familiar with the phrase from high school and college courses that I took over ten years ago. I'm glad to see you will do a Discrete Math course (wish it was sooner, but at least there is one planned). I hope to see a Probability & Statistics course sometime also.
RLH
Udemy student
Very thorough explanation of completing the square. This topic was barely touched on in my pre calc or calculus classes in college.
Peter S.
Udemy student
I'm doing this for revision; I would liek to know it in more detail hence taking advantage of this free course.
Tong L.
Udemy student
Excellent teaching!
Richard H.
Udemy student
Explanations are clear and follow a logical order and path that makes understanding new concepts easier without making known concepts take too long and making the course drag.
James G.
Udemy student
Good explanations and examples.
Eli J.
Udemy student
Brilliant math teacher explains everything so very clearly. Fantastic.
Roberto F.
Udemy student
It was a topic I had already covered in high school. I took this course as a refresher and I really appreciated the clarity of the explanations.
Joseph B.
Udemy student
I have struggled sometimes with this concept and have only recently began to use it when factoring was not practical. This course will help me solidify my skills such that I can share them with others with whom I work.
Chris R.
Udemy student
Calm, clear and just the right amount of detail!!!