Introduction to Quadratic Equations & Solving by Finding Square Roots Chapter 5.3.

Slides:

Advertisements

Similar presentations

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.

Advertisements

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.

Solving Quadratic Equations Using Square Roots & Completing the Square

Day 5 Simplify each expression: Solving Quadratic Equations I can solve quadratic equations by graphing. I can solve quadratic equations by using.

13-1 Introduction to Quadratic Equations  CA Standards 14.0 and 21.0  Quadratic Equations in Standard Form.

Solving Absolute Value Equations By the end of this lesson you will be able to: Solve absolute value equations analytically. GPS MM2A1c.

9.4 – Solving Quadratic Equations By Completing The Square

Solving Quadratic Equations by Completing the Square

SOLVING QUADRATIC EQUATIONS COMPLETING THE SQUARE Goal: I can complete the square in a quadratic expression. (A-SSE.3b)

A radical equation is an equation that contains a radical.

WARM-UP. 8.6 PRACTICE SOLUTIONS(14-33 EVEN) CLEAR UP A FEW THINGS.

Solving Equations by Extracting Roots

Solving Quadratic Equations by Factoring. Solution by factoring Example 1 Find the roots of each quadratic by factoring. factoring a) x² − 3x + 2 b) x².

Table of Contents Solving Quadratic Equations – Square Root Method The square root method can be used to solve a quadratic equation that can be set up.

Solving Quadratic Equations – Square Root Method The square root method can be used to solve a quadratic equation that can be set up into the following.

Solving Quadratic Equations

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.

A Quadratic Equation is an equation that can be written in the form Solving Quadratic Equations – Factoring Method Solving quadratic equations by the factoring.

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.

6.6 Solving Radical Equations. Principle of power: If a = b then a n = b n for any n Question: Is it also true that if a n = b n then a = b? Explain in.

Feb 9 and 10 Solving Square Root Equations. A radical equation is an equation that has a variable in a radicand (or a variable with a fractional exponent)

6.5 Solving Square Root and Other Radical Equations p390.

 Quadratic Equations Solve by Completing the Square.

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

Quadratic Relations Solving Quadratic Equations Day 2: Solve by Isolating the Variable Saturday, June 04, 20161Day 2 - Solve by Isolating the Variable.

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.

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

Martin-Gay, Beginning Algebra, 5ed 22 Not all quadratic equations can be solved as in the previous examples. By using a method called completing the square,

Taking the n th Root to Solve Equations Chapter 7.1.

Solving Radical Equations Chapter 7.6. What is a Radical Equation? A Radical Equation is an equation that has a variable in a radicand or has a variable.

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

Perfect squares: 1, 4, 9, __, __, __, __, __, __, __,…

9.1c SKM & PP 1 Quadratic Equations. 9.1c SKM & PP 2 Square Roots: Know Your Squares! Consider this equation: What number(s) could be squared to give.

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 Simplify each expression. Assume all variables are positive

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

A radical equation is an equation that contains a radical. BACK.

x + 5 = 105x = 10  x = (  x ) 2 = ( 5 ) 2 x = 5 x = 2 x = 25 (5) + 5 = 105(2) = 10  25 = 5 10 = = 10 5 = 5.

9.1 Solving Quadratic Equations by Finding Square Roots.

Algebra 3 Lesson 2.6 Objective: SSBAT solve quadratic equations. Standards: M11.D

Factoring & Solving Quadratics Equations Intermediate Algebra Final Exam Review.

3.4 Chapter 3 Quadratic Equations. x 2 = 49 Solve the following Quadratic equations: 2x 2 – 8 = 40.

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.

SOLVING QUADRATICS: THE SQUARE ROOT PRINCIPLE PART 3.

SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE

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

Equations Quadratic in form factorable equations

Solving Quadratic Equations by the Complete the Square Method

Quadratic Equations, Inequalities, and Functions

Solving Radical Equations

Section 1.6 Other Types of Equations

Appendix A.5 Solving Equations.

Essential Questions Solving Radical Equations and Inequalities

9.3 Solving Quadratic Equations

Do Now 1) t + 3 = – 2 2) 18 – 4v = 42.

Solving Square Roots Unit 3 Day 3.

Solving Radical Equations

Solving Quadratics Using Square Roots

Solving Radical Equations

Quadratic Equations.

9.2 Solving Quadratic Equations using square roots

Equations Quadratic in form factorable equations

Exercise Solve x – 14 = 35. x = 49.

Solving Quadratic Equations by Finding Square Roots

Objective Solve radical equations.. Objective Solve radical equations.

Complete the Square January 16, 2017.

Equations Involving Absolute Value

Presentation transcript:

Introduction to Quadratic Equations & Solving by Finding Square Roots Chapter 5.3

Quadratic Equations Have one variable The variable is raised to the power of 2 (a.k.a. The variable is squared) Examples x 2 = 25 t 2 + 5t + 6 = 0 y 2 – 3 = 2y (x + 2)(x + 3) = 12

Solving Quadratic Equations by Finding Square Roots You can take the square roots of each side to solve some quadratic equations. For example, x 2 = 25 x = ± This is usually written x = ± 5  25

1.Isolate the expression being squared. 2.Take the square root of both sides of the equation. 3.Remember there is often 2 solutions, a positive and a negative. **Leave irrational solutions in “square root form” For example if your solution is x = ± Solving Quadratic Equations by Finding Square Roots 22