Algebra I - PowerPoint Presentation

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Algebra I - PPT Presentation

Chapter 89 Notes Part II 85 86 87 92 93 Section 85 Greatest Common Factor Day 1 Factors Factoring Standard Form Factored Form Section 85 Greatest Common Factor Day 1 ID: 582447

day section function graph section day graph function quadratics factor factoring quadratic functions transformations solving factors number graphing solve parent form related

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Slide1

Algebra I

Chapter 8/9 Notes

Part II

8-5, 8-6, 8-7, 9-2, 9-3Slide2

Section 8-5: Greatest Common Factor, Day 1

Factors –

Factoring –

Standard Form Factored FormSlide3

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 FormSlide4

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 Slide5

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 GCF3) Put the GCFs in a binomial together4) Put the common binomial next to the GCF binomial

Ex) 4qr + 8r + 3q + 6Slide6

Section 8-5: Grouping, Day 2

Factor the following by grouping

rn + 5n – r – 5 2) 3np + 15p – 4n – 20 Slide7

Section 8-5: Grouping, Day 2

Factor by grouping with additive inverses.

1) 2mk – 12m + 42 – 7k

2) c – 2cd + 8d – 4 Slide8

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 variableSlide9

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) Slide10

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 trinomialEx)  (x + 3)(x + 4) Slide11

Section 8-6: Factoring Quadratics,

Day 1

Factor the following trinomials

1) 2) Slide12

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 numberSlide13

Section 8-6: Factoring Quadratics,

Day 1

Factor the following trinomials

1) 2)3) 4) Slide14

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

Solve by factoring and using ZPP.

1) 2)

3) 4) Slide15

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.Slide16

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 LEx) Slide17

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

1) 2)

3) 4) Slide18

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

Factoring using First/Last when c is negative.

1) 2) Slide19

Section 8-7: Factoring Completely,

Day 2

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

1) 2) Slide20

Section 8-7: Solving by Factoring,

Day 2

Solve by factoring

1) 2) Slide21

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) Slide22

Section 9-2: Solving Quadratics by Graphing

Solutions of a Quadratic on a graph:Slide23

Section 9-2: Solving Quadratics by Graphing

Solve the quadratics by graphing. Estimate the solutions.

Ex) Slide24

Section 9-2: Solving Quadratics by Graphing

Solve the quadratics by graphing. Estimate the solutions.

Ex) Slide25

Section 9-2: Solving Quadratics by Graphing

Solve the quadratics by graphing. Estimate the solutions.

Ex) Slide26

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 Slide27