Factoring Using Special Patterns General Algebra II

Slides:



Advertisements
Similar presentations
X and Y intercepts. X-intercept: The point where a line crosses the x-axis. The coordinates are ( x, 0) where x is any number on the x-axis Y-intercept:
Advertisements

4.3 Solve x2 + bx +c = 0 by Factoring
EXAMPLE 1 Solve a linear-quadratic system by graphing Solve the system using a graphing calculator. y 2 – 7x + 3 = 0 Equation 1 2x – y = 3 Equation 2 SOLUTION.
2-3 solving quadratic equations by graphing and factoring
Algebra 1 Notes Lesson 7-2 Substitution. Mathematics Standards -Patterns, Functions and Algebra: Solve real- world problems that can be modeled using.
Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.
3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =
What you will learn A review of all kinds of factoring (yippee)
Factor Special Products April 4, 2014 Pages
Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.
Factor. 1)x² + 8x )y² – 4y – 21. Zero Product Property If two numbers multiply to zero, then either one or both numbers has to equal zero. If a.
Factoring General Trinomials Factoring Trinomials Factors of 9 are: REVIEW: 1, 93, 3.
5 – 2: Solving Quadratic Equations by Factoring Objective: CA 8: Students solve and graph quadratic equations by factoring, completing the square, or using.
8-1 Completing the Square
Martin-Gay, Beginning Algebra, 5ed 22 Not all quadratic equations can be solved as in the previous examples. By using a method called completing the square,
Example 1A Solve the equation. Check your answer. (x – 7)(x + 2) = 0
WARM UP Find the product. 1.) (m – 8)(m – 9) 2.) (z + 6)(z – 10) 3.) (y + 20)(y – 20)
  Different types of Quadratics:  GCF:  Trinomials:  Difference of Squares:  Perfect Square Trinomials: Factoring Quadratics.
Solving Quadratic Equations by Factoring Lesson 5.2.
Section 5-5: Factoring Using Special Patterns Goal: Factor Using Special Patterns.
Warm Up. 4.3 Solve by Factoring Find this in your notes!
Notes Over 10.7 Factoring Special Products Difference of Two Squares.
Objective: Use factoring to solve quadratic equations. Standard(s) being met: 2.8 Algebra and Functions.
1.2 Quadratic Equations. Quadratic Equation A quadratic equation is an equation equivalent to one of the form ax² + bx + c = 0 where a, b, and c are real.
Standard 14 Solve by completing the square. Example One. Instructions: Factor Perfect Square.
Solving Equations by Factoring.
Algebra 1 Warm up #3 Solve by factoring:.
Equations Quadratic in form factorable equations
5-3 Solving Quadratic Equations by Graphing and Factoring Warm Up
Factor the expression. If the expression cannot be factored, say so.
Objectives Solve quadratic equations by factoring.
Section 5.3 Factoring Quadratic Expressions
Bellwork 1) 2) 3) 4) 5) 27 plus some number is 6. What is the number?
Warm - up x2 – 24x 4x(x – 6) 2. 2x2 + 11x – 21 (2x – 3)(x + 7)
8-6 Solving Quadratic Equations using Factoring
Do Now Solve the following systems by what is stated: Substitution
1-5 Equations Goals: Solve equations with one variable
Algebra II Section 4.5a Complete the Square
5-1 Solving Quadratic Equations by Graphing and Factoring SWBAT
Solving Equations by Factoring.
Factoring Using Special Patterns
Warm-up 1. After factoring each expression on your warm-up
Warm Up 1. Name 2 Perfect Square Trinomials. Use your book if necessary. What c makes this a perfect square & factor? 2. x2 – 12x + c 3. x2 + 10x + c.
Warm-Up #7 Find the product 1. (m – 8)(m – 9) m2 – 17m + 72 ANSWER
Chapter 6.4 Completing the Square Standard & Honors
SECTION 9-3 : SOLVING QUADRATIC EQUATIONS
Solving Linear Systems Algebraically
Solving Quadratic Equations
Lesson 9.7 Factor Special Products
Unit 5 Factor Special Products
5.4 Factor and Solve Polynomial Equations
Factor Special Products
Objectives Solve quadratic equations by graphing or factoring.
4.3 Solving Quadratic Equations by Factoring
P4 Day 1 Section P4.
Warm Up Find the x-intercept of each function. 1. f(x) = –3x + 9 3
You can find the roots of some quadratic equations by factoring and applying the Zero Product Property. Functions have zeros or x-intercepts. Equations.
Algebra 2 Ch.3 Notes Page 15 P Solving Systems Algebraically.
Solving Quadratics by Factoring
Solving the Quadratic Equation by Completing the Square
Honors Algebra 2 Chapter 1a Review
Solving Quadratic Equations by Factoring
Equations Quadratic in form factorable equations
Apply the Fundamental Theorem of Algebra
LEARNING GOALS - LESSON 5.3 – DAY 1
5.2 Solving Quadratic Equations by Factoring
3.4 Solve by Factoring (Part 2)
Section P4.
4.3: Solving (Quadratic Equations) by Factoring
Solving Linear Systems by Graphing
Presentation transcript:

Factoring Using Special Patterns General Algebra II Notes 5.5 (Day 2) Factoring Using Special Patterns General Algebra II

Solving Equations with Special Patterns by Factoring: Step 1: Set the equation equal to 0. Step 2: Factor (mono out first if possible, difference of two squares, perfect trinomial squared). Step 3: Set each factored term equal to 0. Step 4: Solve for the solutions.

Solve the equation by factoring.

Solve the equation by factoring.

Solve the equation by factoring.

Solve the equation by factoring.

Solve the equation by factoring.

Finding the zeros of a function: Step 1: Substitute 0 in for y or f(x) Step 2: Factor Step 3: Set each factor equal to zero and solve Step 4: Write your solutions as coordinates ****This is different from solving an equation because there are now two variables (x, y). ****Your solutions should be in coordinate form ( , 0), ( , 0) ****”Zeros” are x – intercepts

Find the zeros of the function.

Find the zeros of the function.

Find the zeros of the function.

Homework: P 252, 50-57, 59-64