Solving Quadratic Equations Using the Zero Product Property March 18, 2014.

Slides:

Advertisements

Similar presentations

Solving Quadratic Equations Using the Zero Product Property

Advertisements

Solving Quadratic Equations using Factoring.  has the form: ax 2 + bx + c = 0 If necessary, we will need to rearrange into this form before we solve!

7-3 Solving Equations Using Quadratic Techniques

Solving Quadratic Equations by Factoring Algebra I.

Solving Equations by Factoring

Solving Quadratic Equations by Factoring

Do Now: Factor x2 – 196 4x2 + 38x x2 – 36 (x + 14)(x – 14)

Notes - Solving Quadratic Equations in Factored Form If ab = 0, then a = 0 or b = 0 If the product of two factors is zero, then at least one of the factors.

Unit 1 Expressions, Equations and Inequalities Copyright © 2014, 2010, 2007 Pearson Education, Inc Quadratic Equations.

DO NOW: FACTOR EACH EXPRESSION COMPLETELY 1) 1) 2) 3)

Previously, we have learned how to factor and have explored various factoring techniques. First, we studied how to find and use the GCF. Next, we looked.

Solving Polynomial Equations – Factoring Method A special property is needed to solve polynomial equations by the method of factoring. If a ∙ b = 0 then.

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

Variables on Both Sides. Visual 5x + 6 = 3x + 12.

Review of Radicals and Quadratic Equations Lesson 9.1.

Example: 3x 2 + 9x + 6. Solving Quadratic Equations.

Solving Equations by Factoring Definition of Quadratic Equations Zero-Factor Property Strategy for Solving Quadratics.

5 – 2: Solving Quadratic Equations by Factoring Objective: CA 8: Students solve and graph quadratic equations by factoring, completing the square, or using.

5-5 Solving Quadratic Equations Objectives:  Solve quadratic equations.

Holt McDougal Algebra 2 Solving Rational Equations and Inequalities Solving Rational Equations and Inequalities Holt Algebra 2Holt McDougal Algebra 2.

Solving Quadratic Equations Quadratic Equations: Think of other examples?

Do Now 1) Factor. 3a2 – 26a + 35.

Example 1A Solve the equation. Check your answer. (x – 7)(x + 2) = 0

SOLVING QUADRATIC EQUATIONS Factoring Method. Warm Up Factor the following. 1. x 2 – 4x – x 2 + 2x – x 2 -28x + 48.

Objective The student will be able to: use the zero product property to solve equations SOL: A.14 Designed by Skip Tyler, Varina High School.

EXAMPLE 1 Solve by equating exponents Rewrite 4 and as powers with base Solve 4 = x 1 2 x – 3 (2 ) = (2 ) 2 x – 3x – 1– 1 2 = 2 2 x– x + 3 2x =

Algebra Review: Solving Quadratic Equations by Factoring.

Table of Contents Solving Polynomial Equations – Factoring Method A special property is needed to solve polynomial equations by the method of factoring.

2.1 – Linear and Quadratic Equations Linear Equations.

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)

§ 6.6 Solving Quadratic Equations by Factoring. Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 Zero Factor Theorem Quadratic Equations Can be.

Solving Equations Containing First, we will look at solving these problems algebraically. Here is an example that we will do together using two different.

Math I UNIT QUESTION: What do solutions of equations represent? Standard: MM1A3 Today’s Question: How do we solve quadratic equations algebraically?

Warm Up Finish your test If you already finished, begin looking at 9.1 – Review of Radicals You can start your homework after you have read the section.

Solving Quadratics Review. We must solve to get x 2 by itself 1 st !

Algebra 3 Lesson 2.6 Objective: SSBAT solve quadratic equations. Standards: M11.D

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

Equations Quadratic in form factorable equations

Using the zero product property to solve equations

Solving Equations by Factoring

5.2: Solving Quadratic Equations by Factoring

5.2 Solving Quadratic Equations by Factoring

Modeling and Equation Solving

Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.

Lesson 4-8 Objective The student will be able to:

A quadratic equation is written in the Standard Form,

Solving Quadratic Equations by Factoring March 16, 2015

Solving Quadratics by Factoring

Notes - Solving Quadratic Equations in Factored Form

4.3 Solving Quadratic Equations by Factoring

Objective The student will be able to:

Using Factoring To Solve

Standard Form Quadratic Equation

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

Solving Quadratic Equations

Algebra 1 Section 12.1.

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

Chapter 6 Section 5.

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

Bellwork: 2/13/18 Find each product.

Warm Up Do Objective 1b, Page 14 in the End of Course Warm Up Booklet

Equations Quadratic in form factorable equations

6.8 Solving Equations by Factoring

Objective The student will be able to:

Warm up Factor Completely 5x2 – 13x + 6 x2 – 9y2 3) y2 + 2y – 48

Solving by Factoring.

Objective The student will be able to:

9-5 Factoring to Solve Quadratic Equations

Objective SWBAT solve polynomial equations in factored form.

Solving Quadratic Equations by Factoring March 11, 2016

Presentation transcript:

Solving Quadratic Equations Using the Zero Product Property March 18, 2014

Can you solve the puzzle below? I’m thinking of two numbers. Their product is zero. Tell me one of the numbers and why you think it is that number.

Can you solve the puzzle below? I’m thinking of two numbers. Their product is zero. Tell me one of the numbers. Write, in your own words, why one of the numbers has to be zero.

Now, let’s think of this algebraically. AB=0 Tell me the value of one of the variables.

Zero Product Property The product of two factors is zero only when at least one of the factors is zero. The product of two factors is zero only when at least one of the factors is zero. If ab = 0, then a=0 or b = 0

Does it matter which one of the variables is zero? Could both of the variables be zero?

Complete the following: Example 1 If (x-2) (x+3) = 0, then _____ = 0 or _____ = 0. Example 2 If x (x-1) = 0, then _____ = 0 or _____ = 0.

Now let’s apply this to solving some equations. (x-4) (x+2) = 0 The expressions have a zero product. x-4=0 or x+2=0 Therefore, one of the numbers must be zero. x=4 or x=-2 Since we do not know which one is equal to zero, we set them both equal to zero and we solve each expression for ‘x’.

Now try a few of these on your own. Solve 1. (x-4)(x-5)=0 2. x(2x+2)(3x-1)=0 3. 2x(x+2)=0

Check your answers. 1. (x-4)(x-5)=0 x=4 or x=5 2. x(2x+2)(3x-1)=0 x=0 or x=-1 or x=1/3 3. 2x(x+2)=0 x=0 or x=-2

Solving quadratic equations X 2 + 7x + 10 = 0 (x + 2)(x + 5) = 0 Factor x + 2 = 0 or x + 5 = 0 Set each to zero X = -2 or x = -5 Solve

Set your equation to zero X 2 + 8x = 65 X 2 + 8x - 65 = 0 Set to zero (x + 13)(x – 5) = 0 Factor X + 13 = 0 or x – 5 = 0 Set to 0 x = -13 or x = 5 Solve x = -13 or x = 5 Solve

Check your answers help/article/solving-quadratic- equations1/#heading1