Homework (Tuesday, 11/3) Lesson 2.03 packet page 4 and 5.

Slides:



Advertisements
Similar presentations
Using the Zero-Product Property to Solve a Quadratic
Advertisements

Solving Quadratic Equations Algebraically Lesson 2.2.
2-4 completing the square
WARM UP What do you remember?.... QUADRATIC EQUATIONS SECTION 5.5.
EXAMPLE 3 Solve an equation by factoring Solve 2x 2 + 8x = 0. 2x 2 + 8x = 0 2x(x + 4) = 0 2x = 0 x = 0 or x + 4 = 0 or x = – 4 ANSWER The solutions of.
5.4 Factoring Quadratic Expressions. WAYS TO SOLVE A QUADRATIC EQUATION ax² + bx + c = 0 There are many ways to solve a quadratic. The main ones are:
Quadratic Equations, Functions, and Models
Solving Quadratic Equations by Factoring
The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)
Factor Special Products April 4, 2014 Pages
Section 4.5 – Quadratic Equations
Algebra II Honors POD Homework: p odds, odds (you must use completing the square), and 77, 83 Find all real solutions for the following:
Section 5.3 Factoring Quadratic Expressions
Solving Equations by Factoring Definition of Quadratic Equations Zero-Factor Property Strategy for Solving Quadratics.
Factoring to Solve Quadratic Equations
5-5 Solving Quadratic Equations Objectives:  Solve quadratic equations.
5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.
4.5 Quadratic Equations Wherever the graph of a function f(x) intersects the x-axis, f(x) = 0. A value of x for which f(x) = 0 is a zero of the function.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations.
Example 1A Solve the equation. Check your answer. (x – 7)(x + 2) = 0
Section 5-4(e) Solving quadratic equations by factoring and graphing.
SOLVING QUADRATIC EQUATIONS Factoring Method. Warm Up Factor the following. 1. x 2 – 4x – x 2 + 2x – x 2 -28x + 48.
Solving equations with polynomials – part 2. n² -7n -30 = 0 ( )( )n n 1 · 30 2 · 15 3 · 10 5 · n + 3 = 0 n – 10 = n = -3n = 10 =
Section 5.3 Factoring Quadratic Expressions Objectives: Factor a quadratic expression. Use factoring to solve a quadratic equation and find the zeros of.
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.
Solving Quadratic Equations By Factoring Medina1.
13.1 Introduction to Quadratic Equations
10.6 – Solving Equations by Factoring Definitions of the Day (DODs) Zero Product Property.
Slide Copyright © 2009 Pearson Education, Inc. 6.9 Continued Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula.
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)
Solving Quadratic Equations by Factoring. Zero-Product Property If ab=0, then either a=0, b=0 or both=0 States that if the product of two factors is zero.
 Standard Form  y = ax 2 + bx + c, where a ≠ 0  Examples › y = 3x 2 › y = x › y = x 2 – x – 2 › y = - x 2 + 2x - 4.
SAT Problem of the Day. 5.3 Factoring Quadratic Expressions 5.3 Factoring Quadratic Expressions Objectives: Factor a quadratic expression Use factoring.
Warm – Up # 9 Factor the following: 1.3x 2 – 2x – 5 2.4x x + 25.
Martin-Gay, Developmental Mathematics 1 Warm-Up #28 (Thursday, 11/12)
CHAPTER 9 LESSON 4 SOLVE POLYNOMIAL EQUATIONS in FACTORED FORM.
9.4: FACTORING TO SOLVE QUADRATIC EQUATIONS. ZERO-PRODUCT PROPERTY WITH EXAMPLES: Zero-Product Property: If ab = 0, then a = 0 or b = 0. ( If the quadratic.
Bellwork 1)Write in standard form. 2) 3)A student is solving an equation by completing the square. Write the step in the solution that appears just before.
Quiz for Solving Mathematical Equations Megan Reichert Click to Start the Quiz!
Algebra 2 cc Section 2.2 Solve quadratic equations by factoring
A factored form of x 2 + 5x - 24 is — A (x − 4)(x + 6) B (x − 3)(x + 8) C (x − 2)(x + 12) D (x − 6)(x + 4) Which of the following equals when factored.
WARM UP What are the solutions of each equation? 1.) x = 4 2.) x = 0 3.) x 2 – 49 = 0.
2.2 Solving Quadratic Equations Algebraically Quadratic Equation: Equation written in the form ax 2 + bx + c = 0 ( where a ≠ 0). Zero Product Property:
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)
Do Now Use the standard form of a quadratic equation to find the a, b and c of each equation. ax2 + bx + c = 0 x2 – 6x + 10 = 0 2x2 + 3x + 4 = 0 x2 –
7.3 Solving Equations Using Quadratic Techniques
The Quadratic Formula..
Solving Equations by Factoring
Objectives Solve quadratic equations by factoring.
5.3 Factoring Quadratics.
Tuesday You need: - Calculator - Whiteboard, marker, eraser.
5.6 – The Quadratic Formula And Ch 5 Review
The Quadratic Formula.
5.4 Factoring Quadratic Expressions
Solving Quadratic Equations by Factoring
Solving Quadratics by Factoring
Warm-Up 5 minutes List all the factors of each number. 1) 10 2) 48
10.4 Solving Equations in Factored Form
Solving Quadratic Equations
Objective Solve quadratic equations by factoring..
Standard Form Quadratic Equation
Solving Quadratic Equations
Warm-Up 5 minutes Factor the following expressions: 2) x2 - 3x
Bellwork #34 April 24th, 2017 Grab a BW sheet from the Algebra I bin.
Homework Lesson 5.3_page 296 # ALL.
The Quadratic Formula..
8.2 Mini-Quiz Review: 6.5a Mini-Quiz Solve Solve.
The Quadratic Formula..
Solving Equations by Factoring
Presentation transcript:

Homework (Tuesday, 11/3) Lesson 2.03 packet page 4 and 5

Lesson 2.03 Zero Product Property

Practice Problems a)f(x)= 3x 2 – 16x – 12 b)f(x)= 4x 2 + 5x – 6 c)f(x)= 4x 2 – 49 d)f(x)= 2x X + 12 Solutions: a)(x-6)(3x+2) b)(x+2)(4x-3) c)(2x+7)(2x-7) d)(x+4)(2x+3)

SHORTCUTS a 2 + 2ab + b 2 (a+b) 2 Example: 9x 2 – 42x + 49 (3x-7)(3x-7)  (3x – 7) 2 Example: 25x x + 81 (5x+9)(5x+9)  (5x + 9) 2 a 2 - 2ab + b 2 (a - b) 2 a 2 - b 2 (a+b)(a - b) Example: x 2 – 64 (x + 8)(x – 8)

Zero-Product Property Zero-Product Property: If pq= 0, then p = 0 or q = 0 ax 2 + bx + c = 0 is called the general form of a quadratic equation

Example given f(x) = x , find the solution

Example given f(x) = 81x , find the solution

Example given 15x 2 = 7x + 2, find the solution

Example

Given x 3 + 3x 2 – 4x – 12, solve for x