1. Algebra-2 Lesson 4-3B (Solving Intercept Form)

2. Quiz 4-1, 4-2 1. What is the vertex of: 2. What is the vertex of:

3. Solving Intercept Form Solving Intercept Form 4-3B

4. Standard Form: Axis of symmetry: Vertex: x-intercepts: (1) (2) “2 nd ” “calculate” “min/max” “2 nd ” “calculate” “zero”

5. Axis of symmetry: Vertex: x-intercepts: (1) (2) “2 nd ” “calculate” “min/max” “2 nd ” “calculate” “zero” Vertex Form:

6. Axis of symmetry: Vertex: x-intercepts: (1) (2) “2 nd ” “calculate” “min/max” (2) “2 nd ” “calculate” “zero” Intercept Form: (1)

7. Your turn: Find the vertex for the following: 1. 2.

8. Product of Two Binomials Know how to multiply two binomials (x – 5)(x + 1) x(x + 1) – 5(x + 1) Distributive Property (two times)

9. Your turn: Multiply the following binomials: 3. 4. 5.

10. Smiley Face I call this method the “smiley face”. (x – 4)(x + 2) = ? Left-most term  left “eyebrow” right-most term  right “eyebrow” “nose and mouth” combine to form the middle term. You have learned it as FOIL.

11. Your turn: Multiply the following binomials: 6. 7. 8.

12. Convert Intercept Form to Standard Form Just multiply the binomials. But why would you want to? (intercept form gives more information)

13. Vocabulary To Factor: split a binomial, trinomial (or any “nomial”) into its original factors. “nomial”) into its original factors. Standard form: Factored form: Intercept form is a standard form that has been factored.

14. Factoring Quadratic expressions: (x – 5)(x + 1) (_ + _)(_ + _)

15. Factoring Quadratic expressions: (x – 5)(x + 1) = ? (x + _)(x + _) -1, 5 5, -1 -5, 1 1, -5 -1, 5 1, -5

16. Factoring Quadratic expressions: (x – 5)(x + 1) = ? (x + _)(x + _) -1, 5 1, -5 (x – 1)(x + 5) (x – 5)(x + 1)

17. (x m)(x n) c = mn (x + 3)(x + 2) Factoring What 2 numbers when multiplied equal 6 and when added equal 5? b = n + m

18. (x m)(x n) (x – 5)(x + 1) Factoring What 2 numbers when multiplied equal -5 and when added equal -4?

19. (x – 2)(x – 4) Factoring What 2 numbers when multiplied equal 8 and when added equal -6?

20. Your Turn: Factor: 7.8.9.

21. They come in 4 types: (x + 3)(x + 1) Both positive 1 st Negative, 2 nd Positive (x – 1)(x – 5) 1 st Positive, 2 nd Negative (x + 8)(x – 2) Both negative (x – 4)(x + 2)

22. Your Turn: Factor: 10.11. 12.13.

23. Vocabulary Solution (of a quadratic equation): The input values that result in the function equaling zero. If the parabola crosses the x-axis, these are the x-intercepts.

24. Solve by factoring: Factor: Set y = 0 Use zero product property to solve.

25. Your Turn: Solve by factoring: 14.15.16.

26. What if it’s not in standard form? Re-arrange into standard form. 3 + 8 = 11 3 * 8 = 24 x = -3 x = -8 x = -8

27. Your Turn: Solve by factoring: 17.18.

28. What if the coefficient of ‘x’ ≠ 1? Solve by factoring: Use “zero product property” to find the x-intercepts

29. Your Turn: Solve 19.20.

30. Special Products Product of a sum and a difference. (x + 2)(x – 2) “conjugate pairs” (x + 2)(x – 2) “nose and chin” are additive inverses are additive inverses of each other. of each other. “The difference of 2 squares.”

31. Your turn: Multiply the following conjugate pairs: 21. (x – 3)(x + 3) 22. (x – 4)(x + 4) “The difference of 2 squares.” “The difference of 2 squares” factors as conjugate pairs.

32. Your Turn: Solve: 23.23.

33. Special Products Square of a sum. (x + 2)(x + 2)

34. Special Products Square of a difference. (x - 4)(x - 4)

35. Your Turn: Simplify (multiply out) 24.25.

36. Your turn: Solve by factoring 26. 27.

37. Vocabulary Quadratic Equation: Root of an equation: the x-value where the graph crosses the x-axis (y = 0). crosses the x-axis (y = 0). Zero of a function: same as root Solution of a function: same as both root and zero of the function. x-intercept: same as all 3 above.

38. Zero Product Property If A= 5, what must B equal? If B = -2, what must A equal? Zero product property: if the product of two factors equals zero, then either: (a)One of the two factors must equal zero, or (b)both of the factors equal zero.

39. Solve by factoring (1) factor the quadratic equation. (1) factor the quadratic equation. (2) set y = 0 (3) Use “zero product property” to find the x-intercepts

40. Solve by factoring (1) factor the quadratic equation. (1) factor the quadratic equation. (2) set y = 0 (3) Use “zero product property” to find the x-intercepts