We continue to study complex numbers and graphing in the complex plane. We finish this chapter today.

With the extra time, we review parabolas, circles, ellipses, and hyperbolas and do some more exercises to refresh students memory.

From the evaluation tests, I see that most of the students do not know about complex numbers, so I decided to add this chapter into this semester. We will spend the next two lessons on complex numbers.

We covered 2/3 of Complex Number chapter. We will finish it next lesson, plus we should have some extra time which I will use to go over some Hyperbola content again.

We study circles, ellipses, and hyperbolas.

A circle is a locus of points in a plane that are a fixed distance from a given point in that plane. The fixed distance is the radius of the circle and the given point is the center.

An ellipse is defined geometrically as: for a given two points F1 and F2 in a plane, for any positive constant k greater than the distance F1F2, the locus of all points P in the plane such that PF1 + PF2 = k.

A hyperbola is defined as: for a given two points F1 and F2 in a plane, for any positive contstant k, the locus of all points P in the plane such that |PF1 – PF2| = k.

We study the common properties of these three kinds.

This is our first lesson for Algebra 2. Students got their textbooks.

Today We study parabolas, with its relationship to quadratic functions.

Three parents came to the class, with two stayed through the class. I welcome the input from the students and the parents.

Parents: please talk to your kid to get his feedback. Examine your kid’s notebook to see how much exercise he/she did in the class.

We started with talking about the geometric definition of a parabola, its basic properties and how to find the function based on the information about vertex, focus, directrix, etc. We did this by looking at a number of problems. Students then got time to work on some problems. We then talked about those problems and solved them in the class.

After the break, we looked at using parabola to solve problems. Again, we looked a few problems before the students worked on a few more. We then talked about those.

Lastly we looked at one of the major applications of parabola: finding the minimum and maximum values of quadratic functions. Again, we studied a few examples, having students work on a few more. We finished after going over those problems again.

This is a pretty fast paced class and I want to make sure that students feel OK. As I told students, they should have notebooks with them, not just note pad. They should get into a habit of taking notes in the class.

Again, please provide your feedback.