algebra i chapter 8/9 notes part ii 8-5, 8-6, 8-7, 9-2, 9-3
TRANSCRIPT
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)