This formula finds the solution(s) for x in any quadratic equation.

Slides:

Advertisements

Similar presentations

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

Advertisements

( ) EXAMPLE 3 Solve ax2 + bx + c = 0 when a = 1

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.

Introduction A trinomial of the form that can be written as the square of a binomial is called a perfect square trinomial. We can solve quadratic equations.

EXAMPLE 1 Solve quadratic equations Solve the equation. a. 2x 2 = 8 SOLUTION a. 2x 2 = 8 Write original equation. x 2 = 4 Divide each side by 2. x = ±

If b2 = a, then b is a square root of a.

SQUARE ROOT METHOD. Simplify Radicals A. Single Ex.

Solving Quadratic Equations – Completing the Square It is assumed you have already watched the slideshow demonstrating how to complete the square on a.

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.

WARM UP What do you remember?.... QUADRATIC EQUATIONS SECTION 5.5.

Solving Quadratic Equations by Completing the Square

EXAMPLE 2 Rationalize denominators of fractions Simplify

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

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.

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.

3.6 Solving Quadratic Equations

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)

5.3 Solving Quadratic Equations by Finding Square Roots.

Solve x x + 49 = 64 by using the Square Root Property.

Get out Homework 9-6 Practice B Answers , , 2.48

10.6 Using the Quadratic Formula – Quadratic Formula Goals / “I can…”  Use the quadratic formula when solving quadratic equations  Choose an appropriate.

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

Then/Now You have already compared fractions and decimals. (Lesson 3–1) Identify and compare numbers in the real number system. Solve equations by finding.

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.

Section 8.2 The Quadratic Formula  The Quadratic Formula  Solving Equations Using the QF  Solving an Equivalent Equation  Solving Functions and Rational.

10-4 Solving Quadratic Equations by Using the Quadratic Formula

10.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Solve Quadratic Equations by the Quadratic Formula.

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

PERFECT SQUARE TRINOMIALS

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.

Warm-Up Exercises EXAMPLE 1 Standardized Test Practice What are the solutions of 3x 2 + 5x = 8? –1 and – A 8 3 B –1 and 8 3 C 1 and – 8 3 D 1 and 8 3 SOLUTION.

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.

Algebra 2 Perfect Squares Lesson 4-6 Part 1. Goals Goal To solve quadratic equations by finding square roots. To solve a perfect square trinomial equation.

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.

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.

Square Roots All positive real numbers have two square roots, a positive and negative square root. All positive real numbers have two square roots, a positive.

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

Solve Quadratic Equations by Completing the Square

5.6 Quadratic Formula & Discriminant

Using the Quadratic Formula to Find Solutions

The Quadratic Formula..

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

EXAMPLE 2 Rationalize denominators of fractions Simplify

Write each expression as a trinomial.

Quadratic Formula Solving for X Solving for quadratic equations.

Solve a quadratic equation

Solve a quadratic equation

Find the x coordinate using -b/2a, then find the y coordinate.

Section 11.2 The Quadratic Formula.

I CAN solve equations using the Quadratic Formula. lesson 9.4a.

The Quadratic Formula.

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

1B.1- Solving Quadratics:

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.

Completing the Square Find each square.

Ex. 1 Solve by factoring. 2x2 + 9x + 7 = 0 6x2 – 3x = 0

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.

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.

The Quadratic Formula..

The Quadratic Formula..

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

Presentation transcript:

This formula finds the solution(s) for x in any quadratic equation.

ax 2 + bx + c = 0 isolate x’s on one side ax 2 + bx = -c divide each term by a Given

complete the square write as a binomial square find common denominator

isolate the x take the square root of both sides combine fractions on the right

separate the radical simplify the denominator combine the fractions

2a

Quadratic Formula Worksheet.pdf 1.Have the students work through the problems in class using the formula. Use calculators to solve the square roots. Solve to three decimal places.(This is necessary to verify answers to calculator portion of the lesson.)

O Turn on calculator O Go to PRGM button O Scroll over to new O Press Enter O Press Alpha O Type QUAD O Press Enter O Press Program O Scroll to I/O O Scroll down to #8 ClrHme O Press Enter

O Press PRGM O Scroll over to I/O O Go to #1 Input press enter O Type “A=“,A (The quotes must be included) O Scroll over to I/O O Go to #1 Input press enter O Type “B=“,B (The quotes must be included) O Scroll over to I/O O Go to #1 Input press enter O Type “C=“,C (The quotes must be included)

O Press PRGM O Scroll over to I/O O Go to #3 Disp O Press Enter O Type “(-B +√(B^2-4AC))/(2A)” O Press PRGM O Scroll over to I/O O Go to #3 Disp O Press Enter O Type “(-B -√(B^2-4AC))/(2A)” O Programming complete.

O The final program should look like this:

O How to get to the Quad Program O Press PRGM O Press Enter O Type in your “A”, “B”, and “C” values you must press enter after each one.

Quadratic Formula Worksheet.pdf 1.Send the same worksheet home with the students to work through the problems with the calculator program in this lesson. Now the students can compare the answers from the in class assignment to the take home calculator assignment.