Algebra Grade 8. Quadratic equations. Collection 1

Master the world of quadratic equations with our engaging Algebra Grade 8 course! Through interactive lessons and practice problems, you'll gain a solid understanding of quadratic equations, their applications, and various problem-solving techniques.

Why choose our course:

• Interactive learning: Engage with the content through interactive quizzes and exercises.
• Real-world applications: Connect mathematical concepts to everyday life.
• Comprehensive coverage: Explore all key topics in quadratic equations.

Course Content:

• Module 1: Quadratic equations
  Lessons 20-26

Expected Outcomes by Course End:

• Recognize: quadratic equations, incomplete quadratic equations, quadratic trinomials, biquadratic equations.
• Provide examples of: quadratic equations of various types, quadratic trinomials.
• Determine: coefficients of a quadratic equation.
• Formulate: the definition of a quadratic equation and a quadratic trinomial, the root of a quadratic trinomial, Vieta's theorem and its converse.
• Write: the formula for the roots of a quadratic equation, the formula for factoring a quadratic trinomial into linear factors.
• Explain: methods of solving incomplete quadratic equations.
• Understand: how the value of the discriminant determines the number of roots of a quadratic equation; the meaning and proof of Vieta's theorem and its converse; the proof of the theorem on factoring a quadratic trinomial; in which case a quadratic trinomial can be factored into linear factors; the method of factoring a polynomial to solve equations, the method of substitution of variables to solve equations, including biquadratic equations.
• Realize that quadratic equations and equations that can be reduced to quadratic equations can serve as mathematical models of real-life situations.
• Compose: quadratic equations and equations that can be reduced to quadratic equations based on the condition of a word problem.
• Solve: problems that involve: finding the roots of various types of quadratic equations; applying Vieta's theorem and its converse; factoring quadratic trinomials; using the factorization of a quadratic trinomial to simplify rational expressions; finding the roots of equations that can be reduced to quadratic equations; composing and solving quadratic equations and equations that can be reduced to them as mathematical models of word problems and applied problems; create a mathematical model of a problem in the form of quadratic equations and equations that can be reduced to quadratic equations; solve situational problems with real data on: traffic safety, calculating a family budget, the possibility of making large purchases, safety and health, practical aspects of financial issues, movement on land and water, labor productivity, the cost of goods, mixtures, and alloys.

By the end of this course, students will have a solid understanding of quadratic equations and be able to apply this knowledge to solve a variety of mathematical problems.