PreCalculus Section 1. 6 Solve quadratic equations by: a. Factoring b

Slides:

Advertisements

Similar presentations

10-7 The Quadratic Formula

Advertisements

2.4 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.

Solving Quadratic Equations Algebraically Lesson 2.2.

Solving Quadratic Equations Using Square Roots & Completing the Square

EXAMPLE 4 Choose a solution method Tell what method you would use to solve the quadratic equation. Explain your choice(s). a. 10x 2 – 7 = 0 SOLUTION a.

Solving Quadratic Equations by Completing the Square.

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations Section 1.3

Section 10.5 – Page 506 Objectives Use the quadratic formula to find solutions to quadratic equations. Use the quadratic formula to find the zeros of a.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 1 Chapter 9 Quadratic Equations and Functions.

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)

SOLVING QUADRATIC EQUATIONS Unit 7. SQUARE ROOT PROPERTY IF THE QUADRATIC EQUATION DOES NOT HAVE A “X” TERM (THE B VALUE IS 0), THEN YOU SOLVE THE EQUATIONS.

Quadratics Solving equations Using “Completing the Square”

2.6 Solving Quadratic Equations with Complex Roots 11/9/2012.

Derivation of the Quadratic Formula The following shows how the method of Completing the Square can be used to derive the Quadratic Formula. Start with.

The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.

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

PreCalculus Section P.1 Solving Equations. Equations and Solutions of Equations An equation that is true for every real number in the domain of the variable.

Completing the Square SPI Solve quadratic equations and systems, and determine roots of a higher order polynomial.

Solve by taking roots. Warm up. Homework Review Completing the Square.

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.

Warm Up 1.) What is the graph of the function y = -x 2 + 4x + 1?

PreCalculus Section 1.6 Solve quadratic equations by: a. Factoring b. Completing the square c. Quadratic formula d. Programmed calculator Any equation.

1.7 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

Completing the Square. Objectives Solve quadratic equations by completing the square.

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.

Solve Quadratic Functions by Completing the Square

Completing the Square, Quadratic Formula

Solve Quadratic Equations by Completing the Square

PreCalculus Section 14.3 Solve linear equations using matrices

The Quadratic Formula..

Aim: What are the properties of a quadratic equation?

The Square Root Principle & Completing the Square

The Quadratic Formula..

Solving Quadratic Equations by Completing the Square

Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

Quadratic Formula Solving for X Solving for quadratic equations.

Solving Quadratic Equations

Factoring Special Cases

Solving Quadratic Equations by Completing the Square

DCA Answers 1. C 2. G 3. B 4. F 5. D 6. F 7. B 8. F 9. B 10. H 11. D

9.3 Solving Quadratic Equations

Section 11.2 The Quadratic Formula.

The Quadratic Formula.

13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

Section 11.1 Quadratic Equations.

9.3 Solve Quadratics by Completing the Square

Sec. 1.4 Quadratic Equations.

2.4 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

5.4 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

Solving Quadratic Equations by Completing the Square

Section 9.2 Using the Square Root Property and Completing the Square to Find Solutions.

The Square Root Property and Completing the Square

Quadratic Equations and Functions

Solving Quadratic Equations

9.2 Solving Quadratic Equations using square roots

Chapter 10 Final Exam Review

13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

4.5: Completing the square

13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

5.4 Completing the Square.

Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

The Quadratic Formula..

6-3 Completing the Square

The Quadratic Formula..

ALGEBRA I : SECTION COMPLETING THE SQUARE

quadratic formula. If ax2 + bx + c = 0 then

Presentation transcript:

PreCalculus Section 1. 6 Solve quadratic equations by: a. Factoring b PreCalculus Section 1.6 Solve quadratic equations by: a. Factoring b. Completing the square c. Quadratic formula Any equation that can be written in the form ax2 + bx + c = 0 is a quadratic equation. It has two solutions. Solve by factoring 3x2 - 2x – 8 = 0 Solve by factoring 2x2 + 7x + 3 = 0

Solve by factoring (3x – 2)(x + 4) = -11

Solve by completing the square 2x2 - 12x - 7 = 0 Procedure Make the leading coefficient one. Isolate the constant. 3. Add the square of ½ the linear coefficient to both sides. Factor the quadratic. Square root and solve.

Solve by completing the square (2x – 1)2 = -4

The solutions to a quadratic equation ax2 + bx + c = 0 can be found by using the quadratic formula. Solve by using the quadratic formula. 2x2 + 7 = 4x

Solve by the quadratic formula. y2 – 8y = 2

Solve by any method = x + 1 r2 + 1 = r + 5 r + 2 3 r+2

assignment Page 35 Problems 1 – 16, 17 -29 not ÷ 3