Introduction to Quadratic Equations and Inequalities for General Studies
The free online course teaches you about quadratic equations and inequalities, as well as various exponential functions.Publisher: ADU
CertificationView course modules
Quadratic equations and inequalities for General Studies is a free online course that has been specifically prepared to teach you about quadratic functions and the different methods of solving quadratic equations. When working with quadratic functions, you should take time to learn about how to solve a quadratic equation by factoring. This course also highlights how to graph a quadratic function. Do you know that quadratic equations can be solved by graphing and by completing the square? Prepare yourself to learn about the various steps involved in the derivation of the quadratic formula and how it's used to solve problems. It is also important that you learn about the discriminant of roots, as well as how to find the sum and product of the roots. You will learn about the relationship between the sum and product of the roots and coefficients of the equation. If you are asked about writing a quadratic equation given its roots, you should know that understanding the nature of roots and the coefficient is important. Are you aware that quadratic equations can also be solved by maximizing area and using the Pythagorean Theorem?
If you want to learn about other methods of solving quadratic equations such as frame problems and projectile motion, then you should complete this course. While going through this course, you will learn about the two methods of solving quadratic-linear systems which include; solving quadratic-linear systems graphically and algebraically. You will also learn about the concepts of quadratic inequalities, as well as how to solve quadratic inequalities. Did you know that quadratic inequalities can be solved using algebraic methods of set theory and number line analysis? To gain a better understanding, you should know the conditions involved in using these methods. You will also be able to identify the concepts of transcendental and trigonometric functions. This course can also help you understand the concepts, definition and properties of exponential functions. The graphing, applications and inverse of exponential functions will be covered extensively in this course. You will become familiar with Type I and Type II exponential functions. It is also imperative that you learn the two methods used to solve exponential equations; either algebraically or graphically.
Furthermore, you can also learn about the definition and properties of logarithmic functions. Do you know that there are two types of logarithms? To gain more insight on this, you will need to understand the concepts of logarithms. You will learn about the five laws of logarithms and natural logarithms. You will also learn about how to plot the graph of a logarithmic function. You will gain insight on how to change between exponential, as well as logarithmic forms and vice versa. You will also be familiar with ways to manipulate logarithmic functions. The derivation of the change of base formula and its applications will be covered in this course. This course will help you understand how to solve logarithmic equations both algebraically and graphically. The application of the logarithmic scale in measuring the acidity of a solution and measuring the intensity of sound waves will also be covered in this course. This course will be of great interest to students, researchers, and anyone with an interest in understanding quadratic equations and inequalities. So, register for this course and start your next learning journey today.Start Course Now
Quadratic Equations and Inequalities
Quadratic Equations and Inequalities - Learning Outcomes
Solving Quadratic Equations by Factoring
The Quadratic Formula
The Nature of Roots
Quadratic Equations and Inequalities - Lesson Summary
Quadratic Equations and Inequalities - Assessment
Exponential and Logarithmic Functions
Exponential and Logarithmic Functions - Learning Outcomes
Application of Exponents and Logarithms
Exponential and Logarithmic Functions - Lesson Summary
Exponential and Logarithmic Functions - Assessment
Upon the successful completion of this course, you should be able to:
- Explain how to solve quadratic equations by factoring and graphing.
- Discuss how to solve quadratic equations by completing the square.
- Distinguish between the definition and properties of exponential and logarithmic functions.
- Explain the graphing of logarithmic and exponential functions.
- Evaluate expressions using logarithms and exponents.
- Describe how to change between exponential and logarithmic forms.
- State the derivation of the quadratic formula.
- Explain how to solve quadratic-linear systems graphically and algebraically.
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