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

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 polynomial Factoring – 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 situation Ex ) Factor out the GCF 1) 2) 3) 4) 15w – 3v

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

Section 8-5: Grouping, Day 2 Factor the following by grouping 1) 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 ZPP (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 trinomial m x n = c the last number in the trinomial Ex)  (x + 3)(x + 4)

Section 8-6: Factoring Quadratics, Day 1 Factor the following trinomials 1) 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 trinomials 1) 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 factoring 1) 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 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)