9.3 Solving Quadratic Equations by the Quadratic Formula.

Slides:

Advertisements

Similar presentations

Solving Quadratic Equations Algebraically Lesson 2.2.

Advertisements

Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x =

7.1 – Completing the Square

4.8 Quadratic Formula and Discriminant

Section 1.5 Quadratic Equations

9.4 – Solving Quadratic Equations By Completing The Square

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

Section 7.2 – The Quadratic Formula. The solutions to are The Quadratic Formula

Solving Quadratic Equations by Factoring. Solution by factoring Example 1 Find the roots of each quadratic by factoring. factoring a) x² − 3x + 2 b) x².

Warm-up Find the missing term to make the following a perfect square trinomial. Why do you think this is called Complete the Square?

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.

4-6 COMPLETING THE SQUARE Ms. Miller. TODAY’S OBJECTIVE To learn to solve quadratic equations by Finding square roots Completing the square.

Solving Quadratic Equations. Solving by Factoring.

Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Quadratic Equations.

Copyright © Cengage Learning. All rights reserved. Quadratic Equations, Quadratic Functions, and Complex Numbers 9.

5.7 Completing the Square. Warm-up #1 Solve Warm-up #2 Solve.

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

Factoring General Trinomials Factoring Trinomials Factors of 9 are: REVIEW: 1, 93, 3.

More about Quadratic Equations November 16, 2009.

Solving a Trigonometric Equation Find the general solution of the equation.

Solve by factoring. x² = - 4 – 5x 2,. Solve by factoring. n² = -30 – 11n -4 and -1.

Notes Over 5.6 Quadratic Formula

Equations involving three terms constant, linear, and square Take square root, factor or use quadratic formula Quadratic Equations.

Deriving the Quadratic Formula. The Quadratic Formula The solutions of a quadratic equation written in Standard Form, ax 2 + bx + c = 0, can be found.

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

Section 1.3 Quadratic Equations 1. 2 OBJECTIVE 1 3.

A-REI Solve equations and inequalities in one variable. 1. Solve quadratic equations in one variable. a. Use the method of completing the square to transform.

Algebra 2 Notes March 23, Do you remember the Quadratic Formula? - Work with the people around you. Brainstorm and try and remember the quadratic.

ANSWERS!. Completing the Square Level 1 Answers Completing the Square Level 2 Answers.

Solving Quadratics Algebra 2 Chapter 3 Algebra 2 Chapter 3.

Notes Over 10.7 Factoring Special Products Difference of Two Squares.

Quadratic Equations A-REI.4 Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots,

Lesson 6.5: The Quadratic Formula and the Discriminant, pg. 313 Goals: To solve quadratic equations by using the Quadratic Formula. To use the discriminant.

1.2 Quadratic Equations. Quadratic Equation A quadratic equation is an equation equivalent to one of the form ax² + bx + c = 0 where a, b, and c are real.

Equations Quadratic in form factorable equations

AIM #1.5: How do we solve quadratic equations?

COMPLETING THE SQUARE.

Solving Quadratic Equations by the Complete the Square Method

4.6 Completing the Square Learning goals

4.6 Completing the Square Learning goals

5.5 Completing the Square.

Sullivan Algebra and Trigonometry: Section 1.3

Warm – Up #11 .

Warmup 1. Solve x2 – 14x + 9 = 0 by completing the square.

5.6 The Quadratic Formula and the Discriminant

Section 1.5 Quadratic Equations

4.8 The Quadratic Formula and the Discriminant

Unit 7 Day 4 the Quadratic Formula.

Completing the Square CA 14.0, 23.0.

Class Notes 11.2 The Quadratic Formula.

The Quadratic Formula.

10.7 Solving Quadratic Equations by Completing the Square

4.7 Complete the Square.

Factoring a Quadratic Expression

5.5 Completing the Square.

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

Warm-Up Factor the following trinomials. What do you notice?

Quadratic Formula & the Discriminant

Aim: How do we use quadratic formula to solve equation?

Quadratic Equations and Functions

Objective - To solve quadratic equations by completing the square.

Quadratic Equations.

Solving Special Cases.

Warm Up: Put on the back of guided notes

Equations Quadratic in form factorable equations

How do I solve quadratic equations by factoring?

Using the Quadratic Formula to Solve Quadratic Equations

Solving Special Cases.

Presentation transcript:

9.3 Solving Quadratic Equations by the Quadratic Formula

Solving Quadratic Equation by Completing the Square

Solving Quadratic Equation by Completing the Square

Your Turn This is (x + 2) 2. Form perfect trinomial squares by adding an appropriate term. x 2 + 4x x 2 – 6x x 2 – 5x This is (x – 3) 2.

Solve by Completing the Square

Example Solve by completing the square: 4x 2 –3 = –4x Solution: 4x 2 –3 = –4x 4x 2 + 4x – 3 = 0

Example – Solution We then use completing the square to solve the equation. cont’d or

Quadratic Formula

Derivation of the Quadratic Formula

Derivation of the Quadratic Formula

Derivation of the Quadratic Formula

Derivation of the Quadratic Formula

Example

Your Turn

Determine if a quadratic equation has real- number solutions

A TV screen is 46-inch wide. The 46-inch screen is measured along the diagonal. The screen is rectangular in shape and is 17 inches wider than is is high. Find the dimensions of a screen. Solution: 1.Let h = height Then, w = h Equation: h 2 + (h + 17) 2 = 46 2 Application