Quadratic Formula.

Slides:

Advertisements

Similar presentations

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 = ±

Advertisements

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.

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

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 =

Solving Quadratic Equations by the Quadratic Formula

Table of Contents First note this equation has "quadratic form" since the degree of one of the variable terms is twice that of the other. When this occurs,

EXAMPLE 2 Rationalize denominators of fractions Simplify

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

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)

Using square roots to solve quadratic equations. 2x² = 8 22 x² = 4 The opposite of squaring a number is taking its square root √ 4= ± 2.

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.

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

Chapter 10.7 Notes: Solve Quadratic Equations by the Quadratic Formula Goal: You will solve quadratic equations by using the Quadratic Formula.

Warm Up. Solving Quadratic Equations by the Quadratic Formula.

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

Table of Contents Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic.

Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic equation.

Standard 20 The Quadratic Formula Example with numbers put in.

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

Notes Over 5.6 Quadratic Formula

EXAMPLE 3 Use the quadratic formula y = 10x 2 – 94x = 10x 2 – 94x – = 10x 2 – 94x – 300 Write function. Substitute 4200 for y. Write.

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

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.

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.

Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation It.

Warm Up. 4.6 Quadratic Formula What THREE methods have we used so far to solve quadratics? Today you will learn the 4 th and LAST method used for solving.

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 Warm up #3 Solve by factoring:.

Warm Ups Term 2 Week 6.

Using the Quadratic Formula to Find Solutions

The Quadratic Formula..

Solving Quadratic Equations by Completing the Square

EXAMPLE 2 Rationalize denominators of fractions Simplify

Write each expression as a trinomial.

Solving Quadratic Equations by the Complete the Square Method

Solving Quadratic Equations by Completing the Square

Solve a quadratic equation

Warm – Up #11 .

Solving Systems of Equations By Substitution

Solving Using Quadratic Equations

Completing the Square

4.8 The Quadratic Formula and the Discriminant

The Quadratic Formula.

Multiplying Binomials

Solving Systems of Equations By Elimination

Factoring With Stick Man, Day Two

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

Objective - To solve quadratic equations by completing the square.

Quadratic Equations.

Adding and Subtracting Polynomials

Solving the Quadratic Equation by Completing the Square

Solving Systems of Equations By Elimination

Completing the Square Algebra Review.

Solving Systems of Equations By Substitution

Quadratic Formula.

Factoring with GCF and DOS

Writing Equations From Two Points

Factoring with GCF and DOS

Solving System of Equations Word Problems

Warm-Up Set 1: Factor. 1) x2 + 6x + 9 2) x2 - 10x + 25 Set 2: Factor.

Adding and Subtracting Polynomials

The Quadratic Formula..

Solving Quadratic Equations by Finding Square Roots

Factoring with DOS.

Presentation transcript:

Quadratic Formula

Table of Contents 46: Warm-Up, Guided Practice 47: How Do I Use the Quadratic Formula to Factor Trinomials?

Warm-Up Solve for the roots: 1. x2 – 9 = 0 2. -x2 + 4 = 3

Warm-Up Answers Solve for the roots: 1. x2 – 9 = 0 2. -x2 + 4 = 3 + 9 ___________ ___________ - 4 - 4 x2 = 9 ___ -1 -x2 = -1 ___ -1 x =  3 x2 = 1 Roots: (3, 0) x =  1 (-3, 0) Roots: (1, 0) (-1, 0)

Learning Intention/Success Criteria LI: We are learning to factor quadratics with the quadratic formula SC: I know how to -simplify square roots -memorize the quadratic formula -locate solutions by using the quadratic formula -use integer operations -substitute values into an equation

EQ: How Do I Factor Quadratics Using Completing the Square? 5/11/2019

Do the quad solve video

The formula for the roots of a quadratic equation Quadratic Formula The formula for the roots of a quadratic equation

Example 1: Solve for the roots: 2x2 + 3x – 9 = 0 A: B: C: 2 3 -9

(-3, 0) Roots:

Guided Practice 1 Use the quadratic formula to solve the equation: 2x2 – 11x + 12 = 0

Guided Practice 1 Use the quadratic formula to solve the equation: 2x2 – 11x + 12 = 0 Roots: (4, 0) (1.5, 0)

Guided Practice 2 Use the quadratic formula to solve the equation: x2 – 4x + 3 = 0

Guided Practice 2 Use the quadratic formula to solve the equation: x2 – 4x + 3 = 0 Roots: (3, 0) (1, 0)

Example 2: Solve for the roots: x2 + 8x – 1 = 0 A: B: C: 1 8 -1

Roots: (0.12, 0) (-8.12, 0)

Guided Practice 3 Use the quadratic formula to solve the equation: 5x2 – x – 2 = 0

Guided Practice 3 Use the quadratic formula to solve the equation: 5x2 – x – 2 = 0 Roots: (0.74, 0) (-0.54, 0)

Guided Practice 4 Use the quadratic formula to solve the equation: 2x2 – 3x – 6 = 0

Guided Practice 4 Use the quadratic formula to solve the equation: 2x2 – 3x – 6 = 0 Roots: (2.64, 0) (-1.13, 0)