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.
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.
This course is intended for high school students.
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.
- 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
- 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