Algebra 2 cc Section 2.2 Solve quadratic equations by factoring

Slides:

Advertisements

Similar presentations

Solving Quadratic Equations by Factoring Algebra I.

Advertisements

6 – 4: Factoring and Solving Polynomial Equations (Day 1)

Solving Quadratic Equations by Completing the Square

Section 10.5 – Page 506 Objectives Use the quadratic formula to find solutions to quadratic equations. Use the quadratic formula to find the zeros of a.

6.5 – Solving Equations with Quadratic Techniques.

Chapter 5 Factoring.

Solving Quadratic Equations by Factoring

2.3 Part 1 Factoring 10/29/2012. What is Factoring? It is finding two or more numbers or algebraic expressions, that when multiplied together produce.

Essential Question: How do you factor a trinomial and how is it used to solve a quadratic equation? Students will write a summary that describes factoring.

Quadratics Solving equations Using “Completing the Square”

Solving Quadratic Equations by Factoring Terminology Zero Factor Theorem Methods for Solving.

Section 4.4 – Factoring Quadratic Expressions Factors of a given number are numbers that have a product equal to the given numbers. Factors of a given.

Solving Quadratic Equations. Solving by Factoring.

Section 5.3 Factoring Quadratic Expressions

Section 4.7 – The Quadratic Formula Students will be able to: To solve equations using the Quadratic Formula To determine the number of solutions by using.

§ 3.6 Solving Quadratic Equations by Factoring. Martin-Gay, Developmental Mathematics 2 Zero Factor Theorem Quadratic Equations Can be written in the.

Chapter 5.2 Solving Quadratic Equations by Factoring.

Holt Algebra Solving Quadratic Equations by Graphing and Factoring A trinomial (an expression with 3 terms) in standard form (ax 2 +bx + c) can be.

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)

Solving Quadratic Equations by Factoring. The quadratic equation is written in the form ax 2 + bx + c = 0 To solve quadratic equations by factoring we.

  Different types of Quadratics:  GCF:  Trinomials:  Difference of Squares:  Perfect Square Trinomials: Factoring Quadratics.

Quadratic Equations – Part Terminology Zero Factor Theorem Methods for Solving.

13.1 Introduction to Quadratic Equations

2.4 part 1 - Basic Factoring I can... - Factor using GCF -Factor a difference of two perfect squares -Factor basic trinomials.

Solving Quadratic Equations. Factor: x² - 4x - 21 x² -21 a*c = -21 b = -4 x + = -21 = x 3x3x x 3 (GCF) x-7 (x – 7)(x + 3)

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities

Warm Up 1.) What is the graph of the function y = -x 2 + 4x + 1?

PreCalculus Section 1.6 Solve quadratic equations by: a. Factoring b. Completing the square c. Quadratic formula d. Programmed calculator Any equation.

SAT Problem of the Day. 5.3 Factoring Quadratic Expressions 5.3 Factoring Quadratic Expressions Objectives: Factor a quadratic expression Use factoring.

 A method for breaking up a quadratic equation in the form ax 2 + bx + c into factors (expressions which multiply to give you the original trinomial).

Solving Quadratic Equations. Find the quadratic equation if the solutions are 3 and -2. x = 3 x = -2 Make them equal zero. x – 3 = 0x + 2 = 0 (x – 3)(x.

Chapter 9 Final Exam Review. Add Polynomials (2x² + x³ – 1) (2x² + x³ – 1) Like Terms terms that have the same variable (2x³ – 5x² + x) + (2x³ – 5x² +

Factoring Trinomials By Grouping Method Factoring 5/17/20121Medina.

Chapter 5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Factoring.

Objective: Use factoring to solve quadratic equations. Standard(s) being met: 2.8 Algebra and Functions.

Factoring Day 1 I can factor a quadratic expression. x 2 + 3x + 2 Rewrite as (x + 1)(x + 2)

Algebra 1 Section 9.1 Evaluate square roots Solve simple quadratic equations Note: 5 2 = 25 and (-5) 2 = 25 so both 5 and -5 are square roots of 25. What.

Algebra 1 Section 10.5 Factor quadratic trinomials and solve quadratic equations A quadratic trinomial takes the form: ax 2 + bx + c Example: (x+3)(x+4)

PreCalculus Section 1. 6 Solve quadratic equations by: a. Factoring b

Square Root Method Trinomial Method when a = 1 GCF

7.3 Solving Equations Using Quadratic Techniques

Objectives Solve quadratic equations by factoring.

5.3 Factoring Quadratics.

Solving Quadratic Equations

POLYPACK REVIEW

Review of Factoring; Quadratic Equations and Rational

The Quadratic Formula.

Factoring Quadratic Functions if a ≠ 1 (Section 3.5)

Solving Quadratics by Factoring

1B.1- Solving Quadratics:

Warm-Up 5 minutes List all the factors of each number. 1) 10 2) 48

Solving Quadratic Equations

6.3 Solving Quadratic Equations by Factoring

Review: 6.5b Mini-Quiz 1. Solve: 9x2 – 100 = 0.

Review: Simplify.

You can find the roots of some quadratic equations by factoring and applying the Zero Product Property. Functions have zeros or x-intercepts. Equations.

Objective Solve quadratic equations by factoring..

Factoring ax2 + bx + c Objective:

Solve. 2x – 7 = 3x c + 9 = c + 1 3m – 12 = m Warm up Solve. 2x – 7 = 3x c + 9 = c + 1 3m – 12 = m.

Algebra 1 Section 12.1.

Warm-Up 5 minutes Factor the following expressions: 2) x2 - 3x

Solve. 2x – 7 = 3x c + 9 = c + 1 3m – 12 = m Warm up Solve. 2x – 7 = 3x c + 9 = c + 1 3m – 12 = m.

Homework Lesson 5.3_page 296 # ALL.

8.2 Mini-Quiz Review: 6.5a Mini-Quiz Solve Solve.

Solving Equations by Factoring

Skills Check Factoring (after the HW Check)

Presentation transcript:

Algebra 2 cc Section 2.2 Solve quadratic equations by factoring Note: 3∙2 = 6, so 2 and 3 are factors of 6 Factoring is the inverse of multiplying . There are several factoring techniques. Factor out the greatest common factor (GCF) 2x2+ 6x 6x3+ 12x2 22x3 - 11x2 + 33x 21y - 7

Difference of Squares Factoring Pattern a2- b2 = (a+b)(a-b) (conjugates) Factor x2 – 9 4x2 - 25 81 – 16y2 5x2 - 20 2u2 + 8u

ax2 + bx + c is a quadratic trinomial Note: (x+2)(x+3) = x2 + 5x + 6, so (x+2) and (x+3) are factors of x2 + 5x + 6 Its factors are in the form (rx+p)(sx+q) where r∙s = a and p∙q = c, and rq+ps = b http://www.youtube.com/watch?v=AMEau9OE6Bs&feature=player_detailpage ax2 + bx + c is a quadratic trinomial Factor x2 + 4x + 3 (x+3)(x+1) x2 - 7x + 10 (x-2)(x-5)

Factor x2 - x – 6 (x-3)(x+2) x2 + 2x – 8 (x+4)(x-2)

Factor 2x2 + 4x + 2 2(x2 + 2x + 1) 2(x+1)(x+1) 3x2 - 17x + 10 (3x – 2)(x – 5) 12x2 - 25x – 7 (4x + 1)(3x – 7)

A Quadratic Equation takes the form: ax2 + bx + c = 0 It has two solutions. Solve x2 - 3x - 4 = 0 To solve a quadratic equation by factoring: Set in standard form ax2 + bx + c = 0 Factor the quadratic Set each factor equal to zero Solve each resulting equation Check solution

Solve k2 + 24k + 144 = 0 2y2 – 4y - 8 = -y2 + y

solve -3b2 + 90 = -3b

assignment Page 260 Problems 65-78 all