1. Algebra 2 – Chapter 5
Quadratics

9. Angry Birds!
Angry Birds follow a parabolic path. Your quest is to find the equation of the parabola to cause the angry bird to hit the pig. Use the given information and the quadratic regression method to find the equation of the curve. All numbers are decimals – round to the thousandths place. When you think your answer is correct, bring it to me to check it on the computer. Groups that successfully find all four equations will earn a prize. (woooo!)

13. Homework: page 245 (1-19, 33-37) odd

14. 5-2 Properties of Parabolas

19. maximum or minimum

20. homework:

26. 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors?
Factor these expressions – Algebra 1 Review – Do you remember?

27. Factoring is rewriting an expression as the product of its factors.
5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors?
Factoring is rewriting an expression as the product of its factors.
The greatest common factor (GCF) of the expression is a common factor of the term of the expression.

28. 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors?
When you factor a quadratic expression in the form ax2 + bx +c you are looking for a pair of factors that multiply to equal ac and add to equal b.

29. 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors?

30. 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors?

31. 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors?

32. 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors?
Homework: page 268 (1-45) every other odd

33. 5-4 solving Quadratic equations
Solving a quadratic equation means finding the values of the variable that make the equation true.
Usually, for a quadratic equation, there are two solutions.
There are several methods to solve quadratic equations:
Factoring
Finding Square Roots
Completing the Square
Using the Quadratic Formula

34. 5-4 solving Quadratic equations
Solving by factoring requires: Setting the equation equal to zero Completely factoring the equation Using the Zero-Product property to find the zeros. Set each factor equal to zero and solve for the variable. This solution is called a zero of the equation because it makes the equation equal zero.
ZERO PRODUCT PROPERTY: If ab = 0 then a = 0 or b = 0
Example: if 𝒙+𝟑 𝒙−𝟕 =𝟎 then 𝒙+𝟑 =𝟎 𝒐𝒓 𝒙−𝟕 =𝟎

35. 5-4 solving Quadratic equations
Standard Form for a Quadratic Equation: 𝒂 𝒙 𝟐 +𝒃𝒙+𝒄=𝟎 𝒙 𝟐 −𝟓𝒙=𝟐𝟒 𝟐 𝒙 𝟐 −𝟏𝟏𝒙+𝟓=−𝟏𝟎
ZERO PRODUCT PROPERTY: If ab = 0 then a = 0 or b = 0
Example: if 𝒙+𝟑 𝒙−𝟕 =𝟎 then 𝒙+𝟑 =𝟎 𝒐𝒓 𝒙−𝟕 =𝟎

36. 5-4 solving Quadratic equations
Use factoring to solve the following equations:
𝒙 𝟐 +𝟕𝒙=𝟏𝟖
𝟐 𝒙 𝟐 +𝟒𝒙=𝟔
𝟏𝟔 𝒙 𝟐 =𝟖𝒙

37. 5-4 solving Quadratic equations
Solving by finding Square Roots is used when there is no linear term.
Rewrite equation as 𝒂 𝒙 𝟐 =𝒄
Isolate 𝒙 𝟐
Find square roots (remember, there are two!)
Example: 𝟓 𝒙 𝟐 −𝟏𝟖𝟎=𝟎
Try These: 𝟒 𝒙 𝟐 −𝟐𝟓=𝟎 𝟑 𝒙 𝟐 =𝟐𝟒 𝒙 𝟐 − 𝟏 𝟒 =𝟎

38. Simplifying Square Roots
𝑎𝑏 = 𝑎 ∙ 𝑏
𝑎 𝑏 = 𝑎 𝑏
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦 48
48 = 16 ∙ 3
=4 3

39. Simplifying Square Roots
Break the number in the radical down to its prime factors – use a factor tree or repeated division. 72 = 9 ∙ 8 = 3 ∙ 3 ∙ 4 ∙ 2 = 3 ∙ 3 ∙ 2 ∙ 2 ∙ 2 Each pair of factors represents a single root that you can solve out of the radical 𝟕𝟐 = 𝟑∗𝟑∗𝟐∗𝟐∗𝟐 =𝟑∗𝟐 𝟐 = 6 𝟐

40. Simplifying Square Roots
Process is true for variables as well Every pair of variables represents a single root variable 𝒃 𝟑 =𝒃 𝒃

41. 5-6 Complex Numbers How do you take the square root of a negative number?
Up until now, there was no way to deal with a root like this: −𝟐𝟓 The letter i is defined as the square root of negative 1, and can be simplified out of a square root. The numeral is rationalized in the usual way −𝟐𝟓 = −𝟏 (𝟐𝟓) =𝒊 𝟐𝟓 =𝟓𝒊 −𝟑𝟔 −𝟏𝟎𝟎 −𝟓𝟎 −𝟒𝟖

42. 5-6 Complex Numbers How do you take the square root of a negative number?

43. 5-6 Complex Numbers How do you take the square root of a negative number?
Use the Complex Number Plane to represent a complex number geometrically. Locate the real part of the complex number on the horizontal axis and the complex part on the vertical axis. 𝟏+𝟑𝒊 −𝟐−𝟐𝒊 −𝟑𝒊

44. 5-6 Complex Numbers How do you take the square root of a negative number?
The absolute value of a complex number is its distance from the origin in the complex number plane.
You can find the absolute value by using the Pythagorean Theorem.
𝒂+𝒃𝒊 = 𝒂 𝟐 + 𝒃 𝟐
Find the absolute value:
𝟑+𝟒𝒊
−𝟐−𝟓𝒊

45. 5-6 Complex Numbers How do you take the square root of a negative number?
When you add or subtract complex numbers you combine the real parts and imaginary parts separately. When you multiply complex numbers you use the rules for multiplying binomials (FOIL) Remember that i2 = -1

46. 5-6 Complex Numbers How do you take the square root of a negative number?

47. 5-6 Complex Numbers How do you take the square root of a negative number?

48. 5-6 Complex Numbers How do you take the square root of a negative number?
Write each answer in a + bi form

50. 5-7 Completing the Square Using perfect squares to solve equations

51. 5-7 Completing the Square Using perfect squares to solve equations
You can solve an equation where one side of the equation is a perfect square by finding square roots.

52. 5-7 Completing the Square Using perfect squares to solve equations
If one side of an equation is not a perfect square, you can rewrite the constant
term to get a perfect square trinomial.
Use this relationship to complete the square:
𝒙 𝟐 +𝒃𝒙+ 𝒃 𝟐 𝟐 = (𝒙+ 𝒃 𝟐 ) 𝟐
𝒙 𝟐 +𝟏𝟎𝒙+

53. 5-7 Completing the Square Using perfect squares to solve equations
Find the missing constant to complete the square: write the factored square.

54. 5-7 Completing the Square Using perfect squares to solve equations

55. 5-7 Completing the Square Using perfect squares to solve equations

56. 5-7 Completing the Square Using perfect squares to solve equations

57. 5-7 Completing the Square Using perfect squares to solve equations

58. 5-7 Completing the Square Using perfect squares to solve equations

59. 5-7 Completing the Square Using perfect squares to solve equations
homework: page 289 (1-33) odd Chapter 5 study guide will be given out at our next class. Chapter 5 Test will be given the Thursday(5th) and Friday (6th) after Thanksgiving break.

61. 5-8 The Quadratic Formula

69. Homework: p 289 (23-33) odd p 297 (1-39) odd