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,

Slides:

Advertisements

Similar presentations

Factor and Solve Quadratic Equations

Advertisements

Chapter 5 Section 4: Complex Numbers. VOCABULARY Not all quadratics have real- number solutions. For instance, x 2 = -1 has no real-number solutions because.

Complex Numbers The imaginary number i is defined as so that Complex numbers are in the form a + bi where a is called the real part and bi is the imaginary.

How do I solve quadratic equations? Notes Over Solving Quadratics Methods of Solving Quadratics Square Root Method: No bx term.

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

Solving Quadratic Equations Using Square Roots & Completing the Square

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.

Objectives: 1. Solve equations by: A. Factoring B. Square Root of Both Sides C. Completing the Square D. Quadratic Formula 2. Solve equations in quadratic.

+ Completing the Square. + In your notes: Simplify the following: (5 – 3i)(4 + 2i) 3.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 9–4) CCSS Then/Now New Vocabulary Key Concept: The Quadratic Formula Example 1:Use the Quadratic.

Solve.. Question of the Day CCGPS Geometry Day 62 ( ) UNIT QUESTION: How are real life scenarios represented by quadratic functions? Today’s.

Pgs For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities,

Solving Quadratic Equations

Solving Quadratic Equations Pulling It All Together.

Factoring and Finding Roots of Polynomials

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.

Section 4.7 – The Quadratic Formula Students will be able to: To solve equations using the Quadratic Formula To determine the number of solutions by using.

Completing the Square and Vertex Form of a Quadratic

  Different types of Quadratics:  GCF:  Trinomials:  Difference of Squares:  Perfect Square Trinomials: Factoring Quadratics.

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

1.3 Quadratic Equations College Algebra: Equations and Inequalities.

Completing the Square. Methods for Solving Quadratics Graphing Factoring Completing the Square Quadratic Formula.

5-7: COMPLEX NUMBERS Goal: Understand and use complex numbers.

Notes Over 5.6 Quadratic Formula

ALGEBRA 2 – CHAPTER 5 QUADRATICS. 5-2 PROPERTIES OF PARABOLAS.

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.

Solving Quadratic Equations. Find the quadratic equation if the solutions are 3 and -2. x = 3 x = -2 Make them equal zero. x – 3 = 0x + 2 = 0 (x – 3)(x.

Solve a quadratic equation by finding square roots

Notes Over 10.7 Factoring Special Products Difference of Two Squares.

A-REI.4 Solve quadratic equations in one variable.

DO NOW: WEDNESDAY APRIL 27 TH Open your Springboard books to 29-1, I’m coming around to check your work and then we’ll check our answers!!!

Completing the Square N-CN.7 Solve quadratic equations with real coefficients that have complex solutions. A-SSE.3 Choose and produce an equivalent form.

 5-Minute Check A. B. C. D. A. B. C. D.. Content Standards A.REI.4 Solve quadratic equations in one variable. a. Use the method of completing the square.

Quadratic Equations. Solving ax 2 + bx + c = 0 Taking Square Roots of Both Sides Graphing Factoring Completing the Square Quadratic Formula.

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.

Warm-Up 1. Find the -Vertex -Y-Intercept -X-intercepts 2. Graph 3. Factor.

Solve Quadratic Functions by Completing the Square

Section 2.5 – Quadratic Equations

Completing the Square, Quadratic Formula

10 Quadratic Equations.

Square Root Method Trinomial Method when a = 1 GCF

Equations Quadratic in form factorable equations

Polynomial Equations and Factoring

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

4.6 Completing the Square Learning goals

Solving Quadratics by Completing the Square

4.6 Completing the Square Learning goals

Warm – Up #11 .

4.4A Factoring: Leading Coefficient ≠1

4.8 The Quadratic Formula and the Discriminant

Complex Numbers Using Complex Conjugates in dividing complex numbers and factoring quadratics -- Week 15 11/19.

Factoring Quadratic Functions if a ≠ 1 (Section 3.5)

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.

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.

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

Objective - To solve quadratic equations by completing the square.

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

Equations Quadratic in form factorable equations

3.4 Solve by Factoring (Part 1)

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

3.6 Solve Quadratics by Finding Square Roots

4.3: Solving (Quadratic Equations) by Factoring

Presentation transcript:

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, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Vocabulary Quadratic Equation: any equation in the form Solution to a quadratic equation: x-intercepts, zeros, roots (where y = 0)

Solving by Factoring

GCF (Greatest Common Factor)

Basic Factoring (Backwards FOIL)

Bottoms Up (Leading Coefficient) Three terms with a number in front Steps: Multiply a and c Replace c with new product and drop a Factor using backwards FOIL Divide both factors by a Bottoms up

Perfect Square Trinomial

Difference of Squares

Review