Minds On: Turn & Talk

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