1. Reminder: you need your text book today!
P.O.D.
Reminder: you need your text book today!
Draw the following sketches on a coordinate grid:
a. a linear increase
b. an exponential growth
c. an exponential decay
d. a quadratic function/parabola
Do you remember our 4-function foldable from unit 1 where we explored different functions in our calculator?

2. Launch copy next slide for students to do this on....
Graph the functions below in your y=
a. y = x2
b. y = x2 + 5
c. y = x2 - 1
d. y = - x2
Talk with your group about what you notice/wonder about the equations above.
Explore the tables to see the differences in the equations. Be specific.

3. BASIC Quadratics Exploration....
a. y = x2
b. y = x2 + 5 x y -2 -1 1 2 x y -2 -1 1 2
Description: (be specific)
Description: (be specific)
c. y = x2 - 1
d. y = - x2 x y -2 -1 1 2 x y -2 -1 1 2
Description: (be specific)
Description: (be specific)

4. To complete the back you might want to also try graphing some equations like these....
y = (x + 3)2
y = (x - 5)2
y = 2x2
y = .5x2
y = (x + 1)2
y = (x - 7)2
y = -5x2

5. Parabola Moves: What makes a quadratic function skinnier? Examples:
What makes a quadratic function wider?
What makes a quadratic function move left/right?
What makes a quadratic function move up/down?

6. Key Learning:
Various representations of quadratic functions (numeric, verbal, graphic, 
symbolic) are used to model and solve real life and mathematical 
applications.
Unit Essential Question:
How can we identify patterns as quadratic, and use tables, graphs, and 
formula to solve contextual problems?
Concept: Quadratic Patterns
What are the characteristics of a quadratic function?
What are the patterns in tables and graphs of quadratic functions?
Vocabulary:
quadratic equation, initial height, initial upward velocity, gravity, projectile, parabola, line of symmetry, maximum, minimum, vertex, concave up, concave down, y intercepts, x intercepts

7. Youtube pumpkin' chunkin videos and show 4-5 minutes to get students interested.....

9. label your paper page 464-467 #'s 1-7 (use today and tomorrow)

11. set this table up in your notebook and complete in groups

14. complete in groups - the summarize whole class

15. complete in groups - the summarize whole class

16. add to journal

17. Page 480
Homework:

18. Quickly copy and complete!!!
P.O.D.
get homework out for a spot-check, then go over it together
Quickly copy and complete!!!
Suppose a pumpkin was launched straight up into the air from a height 
of 30 feet and had an initial upward velocity of 70 feet per second:
1. What rule would combine these conditions and the effect of gravity 
giving a relation between the pumpkin's height, h, and its flight time, t, 
in seconds?
2. How would your rule change if the pumpkin was launched at a 
height of 25 feet with an initial upward velocity of 85 feet per second?

19. Concept: Quadratic Patterns
What are the characteristics of a quadratic function?
What are the patterns in tables and graphs of quadratic functions?
Vocabulary:
quadratic equation, initial height, initial upward velocity, gravity, projectile, parabola, line of symmetry, maximum, minimum, vertex, concave up, concave down, y intercepts, x intercepts

21. Put into L1 and L2

23. Complete in groups

24. POD
During a soccer game a goalie saves a shot. When he kicks the ball it is 2 feet in the air. The soccer ball returned to the ground after 5 seconds. What was the initial upward velocity?

25. Homework:
Page 480

27. POD 1. What two numbers can you add to get 14 and multiply to get 48?

28. Magic Diamond
Product
Integers 8 9
Integers
Sum 1. 2. 3 -4 10

29. Can you find the other integer and the sum?4. 3.
144
-12 -8 2

30. Can you find the integers that form the given product and sum?5. 6. 49 14 22 13

31. 15 16 8
-10

32. 1. 2. 3. 4. 5. 6. 7. 8. 9.
10.
11.
12.

33. 1. 2. 3. 4. 5. 6. 7. 8. 9.
10.
11.
12.

34. POD 1. 2.
-24
-42 -5 11

35. page 423 #'s 30-36
page 524 #'s 30 and 31

36. Page494-495 #4 and CYU Name:_______________
a. Sum:_______________ sketch graph:
Product:______________ Sketch graph:
b. Sum:_______________ sketch graph:
Product:______________ Sketch graph:
c. Sum:_______________ sketch graph:
Product:______________ Sketch graph:
d. Sum:_______________ sketch graph:
Product:______________ Sketch graph:

37. POD Find the velocity of the man as he leaves the cannon.
The cannon is 24 feet off of the ground and the man hits a puffy blow-up mattress, which is 12 feet off of the ground at 6 seconds.
POD

41. POD
Prove/explain if the following equations are equivalent:
4x2 + 6x + 9 and 4x(x + 3) - (2x - 3)

42. page 499 #1
Name:_____________

43. POD
-108
-84
-12 5

47. 2. 6y - y 3. 4m + (7 - m) 4. c - (3c +1) 5. (3r + 4) + (-2r +8)
P.O.D.
Simplify.
1. -9b + 8b
2. 6y - y
3. 4m + (7 - m)
4. c - (3c +1)
5. (3r + 4) + (-2r +8)
6. (-2g + 1) - (2g + 1)
7. (5j - 7k) - (4j - 6k)

48. 5. (6ab)(-2a) + (3ab)(4b) + (-5b)(3ab)
P.O.D.
Simplify.
1. (3x2 + 4x4 - x + 1) + (3x4 + x2 - 6)
2. (5c3 +10c + 5) - (4c3 - c - 1)
3. (10j)(3j)
4. (10j) - (3j)
5. (6ab)(-2a) + (3ab)(4b) + (-5b)(3ab)

49. Foil y = x2 + 19x + 60 y = (x + 7)(x - 4)
Can you do the opposite (factor) this problem?
y = x2 + 19x + 60

50. 9.2 page 436
Use the distributive property. Simplify.
6. 4(x + 2)
7. 8(3x2 - 4x)
8. 3x(2x - 5)
9. x( -x + 5)
10. (x + 4) (x - 5)

51. Foil (multiply binomials)
1. (x + 4)(x + 5)
2. (x - 7) (x + 6)
3. (2x + 5)(x + 8)
F (FIRST)
O (OUTER)
I (INNER)
L (LAST)
4. (x + 3)(x - 4)

53. POD
Get out your homework for a spot check!
Use the FOIL method to find each product.
1. (3x + 2) (5x + 1)
2. (x + 9) (2x - 4)
3. (x + 4) (2x - 5)

54. Concept: Equivalent Quadratic Expressions
How can I expand a factored form?
How can I factor an expanded form?
Vocabulary:
expand, factor, greatest common factor

55. 4. y = x2 - x + 72
5. y = x2 + 11x + 18
6. y = x2 - 13x - 30
7. y = x2 + 17x + 16
8. y = 2x2 + 9x + 10

56. 4. y = x2 - x - 72
5. y = x2 + 15x + 54
6. y = x2 - 13x + 30
7. y = x2 - 29x + 100
8. y = 2x2 + 18x + 40

58. 1. y = x2 + 5x + 6
3. y = 2x2 + 14x + 24
2. y = x2 + 4x + 4

59. 4. y = x2 + 9x + 14
5. y = - x2 + 4x + 5
3. y = (x+3)2

60. y = x2 + 7x + 10 POD - find the intercepts and vertex.
What are you finding when you factor a trinomial?
y = x2 + 7x + 10

61. Concept: Equivalent Quadratic Expressions
How can I expand a factored form?
How can I factor an expanded form?
Vocabulary:
expand, factor, greatest common factor

62. Find the x-intercepts for each:
(by factoring and solving)
1. x2 + 8x + 7
2. x2 -11x + 10
3. x2 + 4x - 12
4. x2 - 4x + 24
5. x2 + 6x + 8
6. x2 - 30x + 40

63. 3. Find the shaded area of the rectangle.
P.O.D.
Find each product.
1. (5x - 6)(5x + 6)
3. Find the shaded area of the rectangle.
2. The rectangle has an area of 63 square centimeters. Find the value of x.
x + 9
x - 9
x + 4
x + 3
x + 2
x - 2

64. Factor each of the following trinomials and then determine the x and y-intercepts.
10. x2 + 5x + 6  x2 - 5x + 6
11. x2 - x - 12  x2 - 5x - 24
12. x2 - 6x + 5  x2 - 11x + 18
13. x2 - 6x + 9  x2 + x - 20
14. x2 - 2x  20. x2 + 7xy + 10y2
15. x2 + 4x - 12 21. x xy + 18y2  

65. Pull out the greatest common factor for each...
12x + 4x2
6m - 30m2
18r + 24

66. Use the FOIL method to find each product. 1. (5p + 3)(p + 1)
P.O.D.
Use the FOIL method to find each product.
1. (5p + 3)(p + 1)
2. (2x + 5)(2x - 3)
3. (a + c)(a + 2c)
4. (x2 + y)(x + y)

67. Greatest Common Factor
What is the greatest common factor for the following?
1. 5 and 30
and 30
and 30
and 45
5. 2x and 6x
6. 3x2 and 9x3

68. Factor the following:
 (2x3) + (4x2) + (6x4)
(2 x x x) + ( x x) + ( x x x x)
2 x x ( x x x)
2x2(x x2)
Answers should be written in order from left to right 
from the greatest exponent to the least exponent.
 2x2(3x2 + x + 2)  

69. Factor the following:
Ex. 1 page 448
7. 5am - 5an
8. 5x3 - 3y2
9. 2c4 - 4c3 + 6c2
Try This
10. 6ab + 3a
11. 5x3 + 10x2 - 20x
12. 2x2 - 3y2
Ex. 2 page 449
13. r(t + 1) + s(t +1)
14. a(x - 3) + 6(x - 3)

70. Factor the following. 1. 3k2 + 21 2. 2y2 - 15y 3. 6c3 + 9c2
P.O.D.
Factor the following.
1. 3k2 + 21
2. 2y2 - 15y
3. 6c3 + 9c2
4. 3x2 + 6x5 + 9x

71. Concept: Equivalent Quadratic Expressions
How can I expand a factored form?
How can I factor an expanded form?
Vocabulary:
expand, factor, greatest common factor

72. P.O.D.
Factor each polynomial.
1. a2 + 12a + 27   (a + 3)(a + 9)
2. k2 + 4k +4   (k +2)(k +2)
3. x2 - 8x + 15   (x - 3)(x - 5)

73. A ball is thrown from 5.5 feet and lands on the ground after 6 seconds. Find the initial velocity.

74. Concept: Equivalent Quadratic Expressions
How can I expand a factored form?
How can I factor an expanded form?
Vocabulary:
expand, factor, greatest common factor

75. 10. (x +2)(x + 3) 11. (x - 4)(x + 3) 12. (x - 5)(x - 1)
Answers #
10. (x +2)(x + 3)
11. (x - 4)(x + 3)
12. (x - 5)(x - 1)
13. (x - 3)(x - 3)
14. (x + 5)(x - 7)
15. (x - 2)(x + 6)
16. (x - 2)(x - 3)
17. (x + 3)(x - 8)
18. (x - 2)(x - 9)
19. (x - 4)(x +5)
20. (x + 5y) (x + 2y)
21. (x - 2y)(x - 9y)

76. Concept: Equivalent Quadratic Expressions
What are the characteristics of a quadratic function?
What are the patterns in tables and graphs of quadratic 
functions?
How can I expand a factored form?
How can I factor an expanded form?

77. Find each product.
1. 5(x - 5)
2. 4y(y + 2)
3. -x(2x - 3)
4. (x + 3)(x - 4)
5. (5d - 8)(d - 1)
6. (4w + 3z)(w + z)
7. (3m + 5)(m + 5)
8. (x + 7)(x - 7)
9. (x + 1)(x +1)
10. (5x - 2)2

78. Factor each polynomial.
11. x3 + 3x2
12. b4 + 15b3 + 5b
m5 + 16m4 - 8m3
14. c2 + 8c + 15
15. m2 - 2m - 8
16. t2 + 8t + 12
17. r2 + r - 56
18. b2 + 11b + 28
19. x2 + 7x + 12

79. 1. 5x - 25
2. 4y2 + 8y
3. -2x2 + 3x
4. x2 - x - 12
5. 5d2 - 13d + 8
6. 4w2 + 7wz + 3z2
7. 3m2 + 20m + 25
8. x2 - 49
9. x2 + 2x + 1
x2 - 20x + 4
11. x2(x + 3)
12. b(b3 + 15b2 + 5)
13. 8m3(3m2 + 2m - 1) = 8m3(3m - 1)(m + 1)
14. (c + 3)(c + 5)
15. (m +2)(m - 4)
16. (t + 2)(t + 6)
17. (r - 7)(r + 8)
18. (b + 4)(b + 7)
19. (x + 3)(x + 4)

80. 9.3 Practice Worksheet
1. a2 + 9a + 20
3. 2t2 + 9t - 18
5. 16c2 - 16c + 3
7. 6p2 - 40p - 14
9. 16x2 - 9
11. r2 - 3r + 2
13. m2 - 8m + 16
15. 2s2 - 3s - 27
c2 - 16cd - 15d2
19. 9x2 - 4y2
21. 6y2 - 5y + 1
s2 + 14s + 1
25. m2 +2mn + n2
x x - 10
29. s4 - t2
31. x2 + 4x - 12