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Understanding Quadratic Equations: Forms and Expansion Techniques

This lesson focuses on quadratic equations, defining their characteristics as second-degree equations where the variable x is squared. Students will learn how to convert between factored and standard forms of quadratic equations using expansion techniques, specifically the FOIL method. We will cover the three different forms of quadratic equations and their relevance. Additionally, visual graphing of quadratics will be discussed, demonstrating the importance of both forms in graphing parabolas effectively. Mastering these concepts will enhance comprehension of algebraic functions.

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Understanding Quadratic Equations: Forms and Expansion Techniques

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  1. Minds On: Turn & Talk • Which of these are QUADRATIC EQUATIONS? • Not Quadratic Quadratic • A quadratic equation is a “second order” or “second degree” equation, meaning the variable x has an exponent of 2 (but not higher than 2) and y always has an exponent of 1.

  2. MFM 2P – Unit 4: Algebra Lesson 1: Expanding Learning Goal: • I can turn factored form quadratic equations into standard form by expanding (FOIL) and simplifying

  3. MFM 2P – Unit 4: Algebra Skills Reminder! “Collecting Like Terms” Lesson 1: Expanding • b)

  4. MFM 2P – Unit 4: Algebra Lesson 1: Expanding Recall: Distributive Property a(b + c) Dog pees EVERYWHERE

  5. MFM 2P – Unit 4: Algebra Lesson 1: Expanding Recall: Distributive Property 3(x – 7) b) -(-2a + b – 3ab) c) -4(3x2– 2x + 4y)

  6. MFM 2P – Unit 4: Algebra Lesson 1: Expanding Expanding means to multiply. Up until now we have multiplied a monomial by a binomial. 4( 5x – 8) Now we will multiply a binomial by a binomial. (x + 2)(x – 8)

  7. MFM 2P – Unit 4: Algebra Lesson 1: Expanding • There are THREE different forms of the QUADRATIC EQUATION • Each is uniquely useful

  8. MFM 2P – Unit 4: Algebra Lesson 1: Expanding • There are THREE different forms of the QUADRATIC EQUATION X-value of vertex X-intercept (“zero”) X-intercept (“zero”) y-value of vertex Y-intercept

  9. MFM 2P – Unit 4: Algebra Lesson 1: Expanding • What happens when a is NEGATIVE?

  10. MFM 2P – Unit 4: Algebra Moving between Factored and StandardForms Lesson 1: Expanding EXPAND Factored Form like y = (x + 2)(x + 4) Standard Form like y = x2 + 6x + 8 FACTOR

  11. MFM 2P – Unit 4: Algebra Lesson 1: Expanding If I gave you this equation: y = x2 – x - 6and asked you to graph it, what would you do?

  12. MFM 2P – Unit 4: Algebra Lesson 1: Expanding If I gave you this equation: y = (x -3)(x +2) and asked you to graph it, what would you do?

  13. MFM 2P – Unit 4: Algebra Lesson 1: Expanding In order to graph a parabola, we need both the standard form and the factored form equations.If we are only given 1 of these equations, we need to change it into the other form so that we have both forms.

  14. MFM 2P – Unit 4: Algebra Lesson 1: Expanding We can use the chart method to expand.

  15. MFM 2P – Unit 4: Algebra Lesson 1: Expanding

  16. MFM 2P – Unit 4: Algebra Lesson 1: Expanding We can also use the chart method when we need to multiply 2 binomials (or in other words: change a factored form equation into standard form).

  17. MFM 2P – Unit 4: Algebra Lesson 1: Expanding

  18. MFM 2P – Unit 4: Algebra Lesson 1: Expanding

  19. MFM 2P – Unit 4: Algebra Lesson 1: Expanding Remember the Dog Pee method? We can use that to multiply two binomials as well! (x + a)(x + b) MULTIPLE Dogs pee EVERYWHERE

  20. MFM 2P – Unit 4: Algebra Lesson 1: Expanding (x + 4)(x – 3) b) (3x + 5)(x – 1)

  21. MFM 2P – Unit 4: Algebra Lesson 1: Expanding We call this method FOIL F – First O – Outside I – Inside L – Last

  22. MFM 2P – Unit 4: Algebra Lesson 1: Expanding Outside First Inside Last

  23. MFM 2P – Unit 4: Algebra Lesson 1: Expanding

  24. MFM 2P – Unit 4: Algebra Lesson 1: Expanding

  25. MFM 2P – Unit 4: Algebra Lesson 1: Expanding y = (x – 2)2

  26. MFM 2P – Unit 4: Algebra Lesson 1: Expanding Consolidation: • Why do we FOIL?

  27. MFM 2P – Unit 4: Algebra Lesson 1: Expanding Remember: • There are THREE different forms of the QUADRATIC EQUATION • Each is uniquely useful

  28. Learning Goals revisited • I can turn factored form quadratic equations into standard form by expanding (FOIL) and simplifying

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