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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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.
Daniel S.
Udemy student
ótima professora.Machine translation: a great teacher.
Chris R.
Udemy student
Calm, clear and just the right amount of detail!!!
Rafiu A.
Udemy student
Absolutely spot on. Dr Hania is wonderful.
Andrés E.
Udemy student
Great course, and Professor Hania is a fantastic instructor. Highly recommended.
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.
Carlos S.
Udemy student
I simply love Professor Hania’s courses. I am learning mathematics like never before. In about two months (taking two free courses and two paid courses), I have already significantly developed my mathematical skills and intuition.

One important point worth mentioning is that, in the paid courses, the Q&A section is outstanding—Professor Hania answers every question in great detail.

I just want to thank her for all the support so far.
Pavel K.
Udemy student
I have seen some of the best like Eddy Woos lectures and this lecture gives me the opportunity to deepen the knowledge and realy think deeper how completing thes square is connected to distributive property that is connected to calculating the Area of a rectangle. Connected learning is the way to go and not blindly following the proceedures. Think about the rools, break them and see that the result change from what we expect.
Great explanation Hania!
Ayush R.
Udemy student
Amazing
Debbie C.
Udemy student
great explanation and friendly, encouraging teacher
Austin H.
Udemy student
Awesome information!