Deriving the Quadratic Formula

Slides:

Advertisements

Similar presentations

STROUD Worked examples and exercises are in the text PROGRAMME F6 POLYNOMIAL EQUATIONS.

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.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. 1. 3x +(– 6x) Warm-Up.

Section 8.1 Completing the Square. Factoring Before today the only way we had for solving quadratics was to factor. x 2 - 2x - 15 = 0 (x + 3)(x - 5) =

Solving Quadratic Equations by Completing the Square

THE QUADRATIC FORMULA It works for everything! …as long as it’s a quadratic equation.

Quadratic Formula Standard Form of a Quadratic Equation ax 2 + bx + c = 0  example  x 2 + 6x + 8 = 0  we learned to solve this by:  factoring  completing.

Pre calculus Problem of the Day Homework: p eoo, odds Factor the following:

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)

Quadratics Solving equations Using “Completing the Square”

Section 8.1 Quadratic Equations  The Graphical Connection  The Principle of Square Roots  Completing the Square  Solving Equations by Completing the.

Solving Quadratic Equations. Solving by Factoring.

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

1. 2. * Often times we are not able to a quadratic equation in order to solve it. When this is the case, we have two other methods: completing the square.

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.

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

Slide Copyright © 2009 Pearson Education, Inc. 6.9 Continued Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula.

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

Ch 10: Polynomials G) Completing the Square Objective: To solve quadratic equations by 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.

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

Martin-Gay, Developmental Mathematics 1 Warm-Up #28 (Thursday, 11/12)

Solving 2 step equations. Two step equations have addition or subtraction and multiply or divide 3x + 1 = 10 3x + 1 = 10 4y + 2 = 10 4y + 2 = 10 2b +

Ch 10: Polynomials G) Completing the Square Objective: To solve quadratic equations by completing the square.

Warm Up  1.) Write 15x 2 + 6x = 14x in standard form. (ax 2 + bx + c = 0)  2.) Evaluate b 2 – 4ac when a = 3, b = -6, and c = 5.

Topic 5 Modeling with Linear and Quadratic Functions 5.7 The Quadratic Formula and the Discriminant.

Solving Quadratic Equations by the Quadratic Formula.

Solve Quadratic Functions by Completing the Square

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

Completing the Square, Quadratic Formula

Solve Quadratic Equations by Completing the Square

The Quadratic Formula..

10 Quadratic Equations.

The Quadratic Formula..

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.

Derivation of the Quadratic Formula

Solving Quadratic Equations by the Complete the Square Method

Solve a literal equation

Solve a quadratic equation

Solving Quadratic Equations by the Quadratic Formula

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

Section 11.2 The Quadratic Formula.

Algebra 1 Section 12.5.

The Quadratic Formula.

10.7 Solving Quadratic Equations by Completing the Square

Section 11.1 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.

9.2 Solving Quadratic Equations using square roots

Completing the Square.

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

3.4 – The Quadratic Formula

4.5: Completing the square

5.4 Completing the Square.

Adapted from Walch Education

The Quadratic Formula..

Solving basic equations

The Quadratic Formula..

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

Ch 10: Polynomials G) Completing the Square

Presentation transcript:

Deriving the Quadratic Formula Complete the square!

The Quadratic Formula The quadratic formula is give you the solutions to ax2 + bx + c = 0 in terms of a, b, and c. The formula: Where did this formula come from? The following slides will show how it’s derived.

Derivation Begin with ax2 + bx + c = 0 . Divide both sides of the equation by a to get x2 + (b/a)x + (c/a) = 0. Subtract c/a from both sides of the equation. x2 + (b/a)x = -c/a

Derivation Continued We have x2 + (b/a)x = -c/a. We want to complete the square on the left side so that we can solve for x. To complete the square, we need to add to both sides of the equation. This gives us

Derivation Continued Notice that is in the form x2+2yx+y2, as we intended. We can factor this as (x+y)2, so we have Now let’s solve for x.

Derivation Continued

Derivation Continued

Derivation Finale