22.3 using the quadratic formula to solve equations answer key

22.3 USING THE QUADRATIC FORMULA TO SOLVE EQUATIONS HOW?Completing the square can derive a formula that can be used to solve any Quadratic equation.DISCRIMINANT* It is b2-4ac*Allows you to find the number of real solutions.EXAMPLE x2-4x+3=0STEP 1: Identify a= 1 b= -4 c= 3 STEP 2: Use b

1.3 Algebraic Expressions

22.3 using the quadratic formula to solve equations answer key
1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,

More information

Factor Polynomials Completely

22.3 using the quadratic formula to solve equations answer key
9.8 Factor Polynomials Completely Before You factored polynomials. Now You will factor polynomials completely. Why? So you can model the height of a projectile, as in Ex. 71. Key Vocabulary factor by grouping

More information

Factoring and Applications

22.3 using the quadratic formula to solve equations answer key
Factoring and Applications What is a factor? The Greatest Common Factor (GCF) To factor a number means to write it as a product (multiplication). Therefore, in the problem 48 3, 4 and 8 are called the

More information

Chapter 6 Quadratic Functions

22.3 using the quadratic formula to solve equations answer key
Chapter 6 Quadratic Functions Determine the characteristics of quadratic functions Sketch Quadratics Solve problems modelled b Quadratics 6.1Quadratic Functions A quadratic function is of the form where

More information

Warm-Up Oct. 22. Daily Agenda:

22.3 using the quadratic formula to solve equations answer key
Evaluate y = 2x 3x + 5 when x = 1, 0, and 2. Daily Agenda: Grade Assignment Go over Ch 3 Test; Retakes must be done by next Tuesday 5.1 notes / assignment Graphing Quadratic Functions 5.2 notes / assignment

More information

FACTORING QUADRATICS 8.1.1 and 8.1.2

22.3 using the quadratic formula to solve equations answer key
FACTORING QUADRATICS 8.1.1 and 8.1.2 Chapter 8 introduces students to quadratic equations. These equations can be written in the form of y = ax 2 + bx + c and, when graphed, produce a curve called a parabola.

More information

A Quick Algebra Review

22.3 using the quadratic formula to solve equations answer key
1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals

More information

7.2 Quadratic Equations

22.3 using the quadratic formula to solve equations answer key
476 CHAPTER 7 Graphs, Equations, and Inequalities 7. Quadratic Equations Now Work the Are You Prepared? problems on page 48. OBJECTIVES 1 Solve Quadratic Equations by Factoring (p. 476) Solve Quadratic

More information

POLYNOMIALS and FACTORING

22.3 using the quadratic formula to solve equations answer key
POLYNOMIALS and FACTORING Exponents ( days); 1. Evaluate exponential expressions. Use the product rule for exponents, 1. How do you remember the rules for exponents?. How do you decide which rule to use

More information

Section 5.0A Factoring Part 1

22.3 using the quadratic formula to solve equations answer key
Section 5.0A Factoring Part 1 I. Work Together A. Multiply the following binomials into trinomials. (Write the final result in descending order, i.e., a + b + c ). ( 7)( + 5) ( + 7)( + ) ( + 7)( + 5) (

More information

Mathematics Placement

22.3 using the quadratic formula to solve equations answer key
Mathematics Placement The ACT COMPASS math test is a self-adaptive test, which potentially tests students within four different levels of math including pre-algebra, algebra, college algebra, and trigonometry.

More information

6.4 Factoring Polynomials

22.3 using the quadratic formula to solve equations answer key
Name Class Date 6.4 Factoring Polynomials Essential Question: What are some ways to factor a polynomial, and how is factoring useful? Resource Locker Explore Analyzing a Visual Model for Polynomial Factorization

More information

Algebra 2: Q1 & Q2 Review

22.3 using the quadratic formula to solve equations answer key
Name: Class: Date: ID: A Algebra 2: Q1 & Q2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which is the graph of y = 2(x 2) 2 4? a. c. b. d. Short

More information

Factoring Polynomials

22.3 using the quadratic formula to solve equations answer key
Factoring Polynomials 8A Factoring Methods 8-1 Factors and Greatest Common Factors Lab Model Factoring 8-2 Factoring by GCF Lab Model Factorization of Trinomials 8-3 Factoring x 2 + bx + c 8-4 Factoring

More information

FACTORING QUADRATIC EQUATIONS

22.3 using the quadratic formula to solve equations answer key
FACTORING QUADRATIC EQUATIONS Summary 1. Difference of squares... 1 2. Mise en évidence simple... 2 3. compounded factorization... 3 4. Exercises... 7 The goal of this section is to summarize the methods

More information

Quadratic Equations and Functions

22.3 using the quadratic formula to solve equations answer key
Quadratic Equations and Functions. Square Root Propert and Completing the Square. Quadratic Formula. Equations in Quadratic Form. Graphs of Quadratic Functions. Verte of a Parabola and Applications In

More information

Florida Math for College Readiness

22.3 using the quadratic formula to solve equations answer key
Core Florida Math for College Readiness Florida Math for College Readiness provides a fourth-year math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness

More information

Factoring. 472 Chapter 9 Factoring

22.3 using the quadratic formula to solve equations answer key
Factoring Lesson 9- Find the prime factorizations of integers and monomials. Lesson 9- Find the greatest common factors (GCF) for sets of integers and monomials. Lessons 9-2 through 9-6 Factor polynomials.

More information

6.3 FACTORING ax 2 bx c WITH a 1

22.3 using the quadratic formula to solve equations answer key
290 (6 14) Chapter 6 Factoring e) What is the approximate maximum revenue? f) Use the accompanying graph to estimate the price at which the revenue is zero. y Revenue (thousands of dollars) 300 200 100

More information

Factoring Quadratic Expressions

22.3 using the quadratic formula to solve equations answer key
Factoring the trinomial ax 2 + bx + c when a = 1 A trinomial in the form x 2 + bx + c can be factored to equal (x + m)(x + n) when the product of m x n equals c and the sum of m + n equals b. (Note: the

More information

Factoring. Key Vocabulary

22.3 using the quadratic formula to solve equations answer key
8 Factoring Find the prime factorization of integers and monomials. Factor polynomials. Use the Zero Product Property to solve equations. Key Vocabulary factored form (p. 41) perfect square trinomials

More information

Algebra I Vocabulary Cards

22.3 using the quadratic formula to solve equations answer key
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

More information

15.1 Factoring Polynomials

22.3 using the quadratic formula to solve equations answer key
LESSON 15.1 Factoring Polynomials Use the structure of an expression to identify ways to rewrite it. Also A.SSE.3? ESSENTIAL QUESTION How can you use the greatest common factor to factor polynomials? EXPLORE

More information

Chapter R.4 Factoring Polynomials

22.3 using the quadratic formula to solve equations answer key
Chapter R.4 Factoring Polynomials Introduction to Factoring To factor an expression means to write the expression as a product of two or more factors. Sample Problem: Factor each expression. a. 15 b. x

More information

How To Factor By Gcf In Algebra 1.5

22.3 using the quadratic formula to solve equations answer key
7-2 Factoring by GCF Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Simplify. 1. 2(w + 1) 2. 3x(x 2 4) 2w + 2 3x 3 12x Find the GCF of each pair of monomials. 3. 4h 2 and 6h 2h 4. 13p and 26p

More information

Polynomial Equations and Factoring

22.3 using the quadratic formula to solve equations answer key
7 Polynomial Equations and Factoring 7.1 Adding and Subtracting Polynomials 7.2 Multiplying Polynomials 7.3 Special Products of Polynomials 7.4 Dividing Polynomials 7.5 Solving Polynomial Equations in

More information

Factoring Polynomials

22.3 using the quadratic formula to solve equations answer key
UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can

More information

Factoring Polynomials

22.3 using the quadratic formula to solve equations answer key
Factoring Polynomials 8A Factoring Methods 8-1 Factors and Greatest Common Factors Lab Model Factorization by GCF 8-2 Factoring by GCF Lab Model Factorization of x 2 + bx + c 8-3 Factoring x 2 + bx + c

More information

FACTORING POLYNOMIALS

22.3 using the quadratic formula to solve equations answer key
296 (5-40) Chapter 5 Exponents and Polynomials where a 2 is the area of the square base, b 2 is the area of the square top, and H is the distance from the base to the top. Find the volume of a truncated

More information

4.1. COMPLEX NUMBERS

22.3 using the quadratic formula to solve equations answer key
4.1. COMPLEX NUMBERS What You Should Learn Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers. Use complex conjugates to write the quotient of two complex numbers

More information

1.3 Polynomials and Factoring

22.3 using the quadratic formula to solve equations answer key
1.3 Polynomials and Factoring Polynomials Constant: a number, such as 5 or 27 Variable: a letter or symbol that represents a value. Term: a constant, variable, or the product or a constant and variable.

More information

Introduction Assignment

22.3 using the quadratic formula to solve equations answer key
PRE-CALCULUS 11 Introduction Assignment Welcome to PREC 11! This assignment will help you review some topics from a previous math course and introduce you to some of the topics that you ll be studying

More information

Lesson 9: Radicals and Conjugates

22.3 using the quadratic formula to solve equations answer key
Student Outcomes Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum. Students convert expressions to simplest radical form.

More information

Algebra II and Trigonometry

22.3 using the quadratic formula to solve equations answer key
Algebra II and Trigonometry Textbooks: Algebra 2: California Publisher: McDougal Li@ell/Houghton Mifflin (2006 EdiHon) ISBN- 13: 978-0618811816 Course descriphon: Algebra II complements and expands the

More information