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


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

h

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

Z
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.
Z
Completing the square in two variables, one at a time, for identifying conic sections: circles, ellipses, parabolas, and hyperbolas.
Z

Completing the square in three variables, one at a time, for identifying quadric surfaces: spheres, ellipsoids, hyperboloids, double cones, etc.

Z
Completing the square in one variable for solving quadratic equations with help of the discriminant and the quadratic formula; derivation of the formula.
Z
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.
Z
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.
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!
Dr. E.
Lecturer
The instructor is extremely pleasant. The pace is perfect, not too fast and not too slow. Everything is crystal clear. Moreover the explanations are highly accurate and the instructor builds a solid foundation before moving on. The applications are interesting too. Great course and great instructor!
James R.
Udemy student
It was a GREAT course!
Andrzej K.
Udemy student
This instructor is one of the best. The presentation of the material is second to none.
Jonathan F.
Udemy student
Thank you so much for taking the time to create these courses!
Daniel S.
Udemy student
excellent
Andrzej P.
Udemy student
A very nice series of lectures on the topic, with many different applications and examples covered. I really liked the worked problems, clear and well explained.
Ayush R.
Udemy student
Amazing
James G.
Udemy student
Good explanations and examples.
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.