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The solutions to a quadratic equation are determined by graphing and finding the x-intercepts.

The solutions to the practice exercise sheet are explained.

Quadratic equations will be solved by 2 factoring methods. The first method is common factor and the second method is sum/product.

Solutions to the practice sheet are explained.

Two new methods of factoring are introduced to be used in solving quadratic equations by factoring.

Solutions to the practice questions are explained.

The application of the quadratic formula is explained through several examples.

The solutions to the lesson 4 practice questions are explained.

Domain, range, vertex, axis of symmetry, intercepts and maximum/minimum values will be discussed.

Solutions to the practice questions are explained.

The solutions to the practice questions are explained.

The 'Completing the Square' method is used to convert a quadratic equation from General Form to Standard Form.

The practice questions on converting from General Form to Standard From are explained.

The solutions to problems involving a quadratic equation and maximum/minimum problems are explained.

Solutions to the practice questions are explained.

The relationship between the exponential graph and the logarithmic graph will be explored. Concepts related to domain, range, intercepts and asymptotes will be discussed.

Solutions to the practice questions are explained.

Converting from exponential form to logarithmic form and vice versa will be discussed; as well as the introduction of the Power Law.

The solutions to the practice questions are explained.

The understanding and application of the Product and Quotient Laws of logarithms will be discussed.

The solutions to the practice questions are explained.

The method for solving exponential and logarithmic equations will be discussed.

The solutions to the practice questions are explained.

Further examples of solving exponential and logarithmic equations will be discussed.

The solutions to the practice questions are explained.

Various examples will illustrate how solving exponential and logarithmic equations can be applied in a real world context.

The solutions to the practice questions are explained.

A formula used for solving problems related to doubling, tripling and half-life will be discussed.

The solutions to the practice questions are explained.

Problems related to compound interest, population and earthquakes will be discussed.

**Course Description**

This course has two sections. The first section, Quadratic Equations and Functions, involves solving quadratic equations. The 3 specific methods discussed are graphing, factoring and employing the quadratic formula. As well, characteristics of quadratic functions, such as vertex, equation of the axis of symmetry, domain, range, intercepts and maximum/minimum values are analyzed.

The second section, Logarithms, introduces the concept of logarithms as it relates to the exponential function. Both functions are illustrated on a graph as inverses of each other. Characteristics such as domain, range, intercepts and asymptotes are analyzed in terms of similarities and differences. The topic of 'change of base' is discussed. Logarithmic laws are introduced and solving logarithmic equations is explained, in relation to the solution of real world problems.

One common thread throughout both sections is understanding the meaning of a point (x,y) on a graph. There are numerous examples, where given a point on the graph, the point is substituted into the equation to find an unknown letter. Often, finding the value of the letter, leads to uncovering further information. Another common thread is understanding the meaning of the mathematical words used in the lessons. At times, lacking correct understanding of terminology can be one of the biggest stumbling blocks to new learning.

**Course Goals**

Upon completion of this course, students will have a solid understanding of the relationship between a quadratic equation and the graph generated by this equation. Students will discover how changing the parameters of an equation will affect the transformation of its respective graph. Students will be able to solve quadratic equations, using various methods. Students will have a strong understanding of logarithms and be able to solve problems related to logarithms.

Students will build their confidence in math.

**Target Audience**

This course is intended for high school students.

**Course Requirements**

Students taking this course should have reasonably strong algebraic skills. They should also have some knowledge of a graphing calculator, particularly in terms of finding zeros and maximum/minimum values.

**Course Includes**

- 5 and a half hours of video lessons
- 15 video lecture lessons
- 15 video exercise review lessons
- 15 quizzes, each having 5 multiple choice questions
- 15 practice sheets
- 12 extra practice sheets
- answers to all quizzes in the resource section
- 3 section summary sheets in the resource section

**Course Topics**

- Solving quadratic equations by graphing
- Solving quadratice equations by factoring
- Solving quadratic equations by using the quadratic formula
- Analyzing characteristics of quadratic functions
- Analyzing transformations
- Converting between forms of quadratic equations
- Comparing the exponential and logarithmic functions
- Change of base
- Converting from exponential form to logarithmic form and vice versa
- Understanding and applying the Power, Product and Quotient laws of logarithms
- Solving logarithmic equations
- Solving problems using logarithmic skills
- Solving problems using a specific formula, related to doubling, tripling and half-life

- Teacher: Phil
- Areas of expertise: High School Mathematics
- Education: Bachelor of Physical Education, Masters of Education
- Interests: Sports, working out, volunteering, kakuro puzzles, spirituality
- Skills: Public Speaking, Leadership
- Associations: Alberta Teachers Association
- Issues I care about: Care for the elderly, Support for marginalized people, Healthy lifestyle choices

For me, teaching is about connecting with students and helping them to be successful learners. Students need to be encouraged to ask questions, to learn from mistakes, to seek extra help and to believe in themselves. A positive attitude and a strong work ethic are huge factors in achieving success.

An answer sheet for all of the quizzes is provided.

A list of common errors and a number of important exponential and logarithmic rules are compiled.

A summary of the various methods of solving quadratic equations is given.

The key points of quadratic functions are listed.