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?

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.

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)

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

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?

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

Youtube pumpkin' chunkin videos and show 4-5 minutes to get students interested..... https://prezi.com/f_8mksaqatir/quadratics/

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

set this table up in your notebook and complete in groups

complete in groups - the summarize whole class

complete in groups - the summarize whole class

add to journal

Page 480 Homework:

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?

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

Put into L1 and L2

Complete in groups

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?

Homework: Page 480

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

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

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

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

15 16 8 -10

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

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

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

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

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:

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

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

page 499 #1 Name:_____________

POD -108 -84 -12 5

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)

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)

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

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)

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)

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)

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

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

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

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

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

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

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

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

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

Factor each of the following trinomials and then determine the x and y-intercepts. 10. x2 + 5x + 6  16. x2 - 5x + 6 11. x2 - x - 12  17. x2 - 5x - 24 12. x2 - 6x + 5  18. x2 - 11x + 18 13. x2 - 6x + 9  19. x2 + x - 20 14. x2 - 2x - 35  20. x2 + 7xy + 10y2 15. x2 + 4x - 12 21. x2 + - 11xy + 18y2  

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

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)

Greatest Common Factor What is the greatest common factor for the following? 1. 5 and 30 2. 10 and 30 3. 20 and 30 4. 30 and 45 5. 2x and 6x 6. 3x2 and 9x3

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

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)

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

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

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)

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

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

10. (x +2)(x + 3) 11. (x - 4)(x + 3) 12. (x - 5)(x - 1) Answers #10 - 21 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)

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?

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

Factor each polynomial. 11. x3 + 3x2 12. b4 + 15b3 + 5b 13. 24m5 + 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

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 10. 25x2 - 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)

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 17. 15c2 - 16cd - 15d2 19. 9x2 - 4y2 21. 6y2 - 5y + 1 23. 49s2 + 14s + 1 25. m2 +2mn + n2 27. 0.02x2 - 0.8x - 10 29. s4 - t2 31. x2 + 4x - 12