Create And Solve Quadratic Equations
Overview
Quadratic equations describe the shape of a thrown ball, the area of a rectangle and countless other situations where a quantity depends on the square of another. Solving them means finding the values that make the equation true, and there is more than one route to the answer.
In this lesson you will create quadratic equations from problems and solve them four ways: by inspection, by factoring, by the quadratic formula, and by completing the square. Knowing all four lets you pick the fastest method for each equation and check one against another.
Objectives
- Create and solve quadratic equations by inspection, factorization, the quadratic formula and completing the square.
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Flashcards
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Create And Solve Quadratic Equations. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- Solve x^2 + 5x + 6 = 0. A. x = 2 or x = 3 B. x = -2 or x = -3 C. x = -1 or x = -6 D. x = 2 or x = -3 Answer: B
- Using the quadratic formula on 2x^2 + 3x - 2 = 0, the solutions are: A. x = 1/2 or x = -2 B. x = 2 or x = -1/2 C. x = -1 or x = 2 D. x = 1 or x = -2 Answer: A
- What is the discriminant of x^2 + 6x + 5 = 0? A. 11 B. 16 C. 36 D. 56 Answer: B
- Completing the square, x^2 + 6x + 5 becomes: A. (x + 3)^2 + 5 B. (x + 6)^2 - 31 C. (x + 3)^2 - 4 D. (x + 3)^2 + 4 Answer: C
- In the quadratic formula, the part b^2 - 4ac is called the: A. root B. coefficient C. discriminant D. constant Answer: C
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