Solve Quadratic Equations by Completing the Square

Slides:

Advertisements

Similar presentations

4.3 Solve x2 + bx +c = 0 by Factoring

Advertisements

How do I solve quadratic equations? Notes Over Solving Quadratics Methods of Solving Quadratics Square Root Method: No bx term.

Warm Up Simplify. Solve by factoring x = –4

Warm Up Simplify

Do Now: Pass out calculators.

EXAMPLE 1 Solve a quadratic equation by finding square roots Solve x 2 – 8x + 16 = 25. x 2 – 8x + 16 = 25 Write original equation. (x – 4) 2 = 25 Write.

Section 4.6 – Completing the Square Students will be able to: To solve equations by completing the square To rewrite functions by completing the square.

SOLVING QUADRATIC EQUATIONS COMPLETING THE SQUARE Goal: I can complete the square in a quadratic expression. (A-SSE.3b)

EXAMPLE 4 Solve a multi-step problem CRAFTS You decide to use chalkboard paint to create a chalkboard on a door. You want the chalkboard to have a uniform.

Warm Up Write each expression as a trinomial. Factor each expression.

4.7 – Complete the Square In lesson 4.5, you solved equations of the form x2 = k by finding the square roots. This method also works if one side of an.

1 What you will learn  How to get a quadratic function from standard form to vertex form  How to solve a quadratic equation using “completing the square”

Algebra Core Review Day 7

What you will learn A review of all kinds of factoring (yippee)

Completing the Square (For help, go to Lessons 9-4 and 9-7.) Find each square. 1.(d – 4) 2 2.(x + 11) 2 3.(k – 8) 2 Factor. 4.b b t t.

2.13 Warm Up x² - 2x + 15 = 0; 3 x² + 3x – 4 = 0; 1

Unit 2 Solving Polynomials by Taking the Square Root.

Unit 5 Algebra Investigations Notes 2.13: Use Square Roots to Solve Quadratic Equations Lesson 3: Solving Polynomials MM1A3a.

2.13 Use Square Roots to Solve Quadratics Example 1 Solve quadratic equations Solution Write original equation. 5 Solve the equation. Add __ to each side.

Completing the Square 4-6 Day 1 Today’s Objective: I can use the process of completing the square to solve or rewrite a quadratic equation.

Factoring and Solving Polynomial Equations (Day 1)

Section 5.4 Day 5 Obj: to factor special and combo quadratic expressions.

4.3 “Solve x 2 + bx + c by Factoring” Vocabulary to Know: Monomial Binomial Trinomial Roots of a Function Zeros of a Function Use FOIL to multiply the.

10.5 & 10.5 Extension 10.5 Solve Quadratic Equations by Completing the Square 10.5 Extension Write Quadratic Functions in Vertex form and Graph the Functions.

Solve each quadratic equation by factoring. 1. x2 + 8x + 16 = 0 2. x2 – 22x = 0 3. x2 – 12x + 36 = 0.

CONFIDENTIAL 1 Completing the Square Completing the Square.

Opener-SAME SHEET-9/21 Find vertex and describe transformation

8-1 Completing the Square

9.5 - The Quadratic Formula

7-6 USING THE QUADRATIC FORMULA ALGEBRA 1 CP OBJECTIVE: USING THE QUADRATIC FORMULA TO SOLVE QUADRATIC EQUATIONS.

Section 10.6 Factoring Objectives: Factor a quadratic expression of the form Solve quadratic equations by factoring.

Section 5-5: Factoring Using Special Patterns Goal: Factor Using Special Patterns.

Essential Question: How is the process of completing the square used to solve quadratic equations? Students will write a summary of how they use completing.

Section 7.2 Solving Quadratic Equations by Completing the Square.

Solve a quadratic equation by finding square roots

Solving Quadratics Algebra 2 Chapter 3 Algebra 2 Chapter 3.

Notes Over 10.7 Factoring Special Products Difference of Two Squares.

Standard 8 Solve a quadratic equation Solve 6(x – 4) 2 = 42. Round the solutions to the nearest hundredth. 6(x – 4) 2 = 42 Write original equation. (x.

Solve Quadratic Equations by Completing the Square

Complete the square to form a perfect square trinomial. 1. x x + 2. x 2 – 18x + Solve by completing the square. 3. x 2 – 2x – 1 = x 2 + 6x.

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.

Do Now Factor the expression. x2 + 18x + 81 x2 - 22x

Chapter 4: Quadratic Functions and Equations

Solve Quadratic Equations by Completing the Square

Notes Over 10.8 Methods of Factoring Binomial Trinomial

A B C D Solve x2 + 8x + 16 = 16 by completing the square. –8, 0

Objectives Solve quadratic equations by completing the square.

Write each expression as a trinomial.

Solving Quadratic Equations by the Complete the Square Method

5.5 Completing the Square.

Completing the Square (3.2.3)

Section 4.7 Complete the Square.

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.

EXAMPLE 1 Complete the square

Section 1.5 Quadratic Equations

Squares of Binomials Chapter 5 Section 5.6.

4.7 Complete the Square.

9.3 Solve Using Square Roots

Factoring a Quadratic Expression

5.5 Completing the Square.

Completing the Square Find each square.

3.4 Solving Simple Quadratic Equations, Completing the Square, and Solving Equations using Completing the Square.

The Square Root Property and Completing the Square

Taking the Square Root of Both Sides (3.2.1)

The constant is always the square of half

The constant is always the square of half Or

How do I solve quadratic equations by factoring?

Factoring Quadratic Expressions

Solve Quadratic Equations by the Quadratic Formula

Presentation transcript:

Solve Quadratic Equations by Completing the Square Section 10.5

Objectives: Solve quadratic equations by finding completing the square

Key Vocabulary: Completing the square Perfect square trinomial

Completing the Square

Example 1: Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.

#1: Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.

#2: Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.

#3: Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.

Example 2: Solve by completing the square.

Example 3: Solve by completing the square.

#4: Solve the equation by completing the square #4: Solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.

#5: Solve the equation by completing the square #5: Solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.

#6: Solve the equation by completing the square #6: Solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.

Example 4: You decide to use chalkboard paint to create a chalkboard on a door. You want the chalkboard to have a uniform border as shown. You have enough chalkboard paint to cover 6 square feet. Find the width of the border to the nearest inch.

Homework Assignment Page 666 #6, 8, 10, 12, 14, 20, 22, 24, 28, 30, 34, 36, 38, 46, 48, 62, 64