1. Chapter 8/9 Notes Part II 8-5, 8-6, 8-7, 9-2, 9-3
Algebra I
Chapter 8/9 Notes
Part II
8-5, 8-6, 8-7, 9-2, 9-3

2. Section 8-5: Greatest Common Factor, Day 1
Factors – Factoring – Standard Form Factored Form

3. Section 8-5: Greatest Common Factor, Day 1
Factors – the numbers, variables, or expressions that when multiplied together produce the original polynomial Factoring – The process of finding the factors of a polynomial Standard Form Factored Form

4. Section 8-5: GCF, Day 1
Greatest Common Factor (GCF): The largest factor in a polynomial. Factor this out FIRST in every situation Ex ) Factor out the GCF 1) 2) 3) 4) 15w – 3v

5. Section 8-5: Grouping, Day 2
Factoring by Grouping 1) Group 2 terms together and factor out GCF 2) Group remaining 2 terms and factor out GCF 3) Put the GCFs in a binomial together 4) Put the common binomial next to the GCF binomial
Ex) 4qr + 8r + 3q + 6

6. Section 8-5: Grouping, Day 2
Factor the following by grouping 1) rn + 5n – r – 5 2) 3np + 15p – 4n – 20

7. Section 8-5: Grouping, Day 2
Factor by grouping with additive inverses. 1) 2mk – 12m + 42 – 7k 2) c – 2cd + 8d – 4

8. Section 8-5: Zero Product Property, Day 3
What is the point of factoring? It is a method for solving non-linear equations (quadratics, cubics, quartics,…etc.) Zero Product Property – If the product of 2 factors is zero, then at least one of the factors MUST equal zero.
Using ZPP: 1) Set equation equal to __________. 2) Factor the non-zero side 3) Set each __________ equal to ___________ and solve for the variable

9. Section 8-5: Zero Product Property, Day 3
Solve the equations using the ZPP
(x – 2)(x + 3) = 0 2) (2d + 6)(3d – 15) = 0
3) )

10. Section 8-6: Factoring Quadratics, Day 1
Factoring quadratics in the form: Where a = 1, factors into 2 binomials: (x + m)(x + n) m + n = b the middle number in the trinomial m x n = c the last number in the trinomial Ex)  (x + 3)(x + 4)

11. Section 8-6: Factoring Quadratics, Day 1
Factor the following trinomials 1) 2)

12. Section 8-6: Factoring Quadratics, Day 1
Sign Rules:
 ( )( )
 ( )( )
 ( )( )
*If b is negative, the – goes with the bigger number
*If b is positive, the – goes with the smaller number

13. Section 8-6: Factoring Quadratics, Day 1
Factor the following trinomials 1) 2) 3) 4)

14. Section 8-6: Solving Quadratics by Factoring, Day 2
Solve by factoring and using ZPP. 1) 2) 3) 4)

15. Section 8-6: Solving Quadratics by Factoring, Day 2
Word Problem: The width of a soccer field is 45 yards shorter than the length. The area is 9000 square yards. Find the actual length and width of the field.

16. Section 8-7: The First/Last Method, when a does not = 1, Day 1
First/Last Steps: 1) Set up F, write factors of the first number (a) 2) Set up L, write factors of the last number (c) 3) Cross multiply. Can the products add/sub to get the middle number (b)? If not, try new numbers for F and L
Ex)

17. Section 8-7: The First/Last Method, when a does not = 1, Day 1
1) 2) 3) 4)

18. Section 8-7: The First/Last Method, when a does not = 1, Day 3
Factoring using First/Last when c is negative. 1) 2)

19. Section 8-7: Factoring Completely, Day 2
You must factor out a GCF FIRST! Then factor the remaining trinomial into 2 binomials. 1) 2)

20. Section 8-7: Solving by Factoring, Day 2
Solve by factoring 1) 2)

21. Section 8-7: Solving by Factoring, Day 2
Lastly…Not all quadratics are factorable. These are called PRIME. It does not mean they don’t have a solution, it just means they cannot be factored. Ex)

22. Section 9-2: Solving Quadratics by Graphing
Solutions of a Quadratic on a graph:

23. Section 9-2: Solving Quadratics by Graphing
Solve the quadratics by graphing. Estimate the solutions. Ex)

24. Section 9-2: Solving Quadratics by Graphing
Solve the quadratics by graphing. Estimate the solutions. Ex)

25. Section 9-2: Solving Quadratics by Graphing
Solve the quadratics by graphing. Estimate the solutions. Ex)

26. Section 9-3: Transformations of Quadratic Functions, Day 1
Transformation – Changes the position or size of a figure on a coordinate plane Translation – moves a figure up, down, left, or right, when a constant k is added or subtracted from the parent function

27. Section 9-3: Transformations of Quadratic Functions, Day 1

28. Section 9-3: Transformations of Quadratic Functions, Day 1
Describe how the graph of each function is related to the graph of . First graph the parent function, then graph the given function. a) b)

29. Section 9-3: Transformations of Quadratic Functions, Day 1

30. Section 9-3: Transformations of Quadratic Functions, Day 1
Describe how the graph of each function is related to the graph of . First graph the parent function, then graph the given function. a) b)

31. Section 9-3: Transformations of Quadratic Functions, Day 1
Describe how the graph of each function is related to the graph of . First graph the parent function, then graph the given function. a) b)

32. Section 9-3: Transformations of Quadratic Functions, Day 2

33. Section 9-3: Transformations of Quadratic Functions, Day 2
Describe how the graph of each function is related to the graph of . First graph the parent function, then graph the given function. a) b)

34. Section 9-3: Transformations of Quadratic Functions, Day 2

35. Section 9-3: Transformations of Quadratic Functions, Day 2
Describe how the graph of each function is related to the graph of . First graph the parent function, then graph the given function. a) b)

36. Section 9-3: Transformations of Quadratic Functions, Day 2

37. Section 9-3: Transformations of Quadratic Functions, Day 2
1) 2) 3) 4) 5) 6)

38. Section 9-3: Transformations of Quadratic Functions, Day 2
Horizontal Translation (h) :
If (x – h) move h spaces
to the right
If (x + h), move h
Spaces to the left
Vertical Translation (k):
If k is positive, move k
Spaces up
If k is negative, move
k spaces down
Reflection (a)
If a is positive, graph
Opens up
If a is negative, graph
Opens down
Dilation (a)
If a is greater than 1,
There is a vertical stretch
(skinny)
If 0 < a < 1, there is a
Vertical compression
(fat)