Algebra I

Chapter 8/9 NotesPart II

8-5, 8-6, 8-7, 9-2, 9-3

Section 8-5: Greatest Common Factor, Day 1

Factors –

Factoring –

Standard Form Factored Form

Section 8-5: Greatest Common Factor, Day 1

Factors – the numbers, variables, or expressions that when multiplied together produce the original polynomialFactoring – The process of finding the factors of a polynomial

Standard Form Factored Form

Section 8-5: GCF, Day 1

Greatest Common Factor (GCF): The largest factor in a polynomial. Factor this out FIRST in every situationEx ) Factor out the GCF1) 2)

3) 4) 15w – 3v

Section 8-5: Grouping, Day 2

Factoring by Grouping1) Group 2 terms together and factor out GCF2) Group remaining 2 terms and factor out GCF3) Put the GCFs in a binomial together4) Put the common binomial next to the GCF binomial

Ex) 4qr + 8r + 3q + 6

Section 8-5: Grouping, Day 2

Factor the following by grouping1) rn + 5n – r – 5 2) 3np + 15p – 4n – 20

Section 8-5: Grouping, Day 2

Factor by grouping with additive inverses.1) 2mk – 12m + 42 – 7k

2) c – 2cd + 8d – 4

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

Section 8-5: Zero Product Property, Day 3

Solve the equations using the ZPP1) (x – 2)(x + 3) = 0 2) (2d + 6)(3d

– 15) = 0

3)4)

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 trinomialm x n = c the last number in the trinomialEx) (x + 3)(x + 4)

Section 8-6: Factoring Quadratics, Day 1

Factor the following trinomials1)

2)

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

Section 8-6: Factoring Quadratics, Day 1

Factor the following trinomials1)

2)

3)4)

Section 8-6: Solving Quadratics by Factoring, Day 2

Solve by factoring and using ZPP.1)

2)

3)4)

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.

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)

Section 8-7: The First/Last Method, when a does not = 1, Day 1

1)2)

3)4)

Section 8-7: The First/Last Method, when a does not = 1, Day 3

Factoring using First/Last when c is negative.1)

2)

Section 8-7: Factoring Completely, Day 2

You must factor out a GCF FIRST! Then factor the remaining trinomial into 2 binomials.1)

2)

Section 8-7: Solving by Factoring, Day 2

Solve by factoring1)

2)

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)

Section 9-2: Solving Quadratics by Graphing

Solutions of a Quadratic on a graph:

Section 9-2: Solving Quadratics by Graphing

Solve the quadratics by graphing. Estimate the solutions.Ex)

Section 9-2: Solving Quadratics by Graphing

Solve the quadratics by graphing. Estimate the solutions.Ex)

Section 9-2: Solving Quadratics by Graphing

Solve the quadratics by graphing. Estimate the solutions.Ex)

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

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

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)

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

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)

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)

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

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)

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

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)

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

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

1) 2)3)

4) 5) 6)

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 kSpaces up

• If k is negative, move k spaces down

Reflection (a)• If a is positive, graphOpens up

• If a is negative, graphOpens 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)