5.6.2 – Solving Quadratics with Square Roots. Yesterday, we looked at the properties of square roots 1) Multiplication Property 2) Division Property 3)

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

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.

Solving Quadratic Equations Using Square Roots & Completing the Square

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

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)

5.7.1 – Complex Numbers. We used the method of square roots to solve specific types of quadratics Only used when we had problems such as x 2 – 16 = 0.

Ch 9: Quadratic Equations B) Square Roots Objective: To solve quadratic equations using square roots.

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.

5.6.1 – Square Root Method. Recall, we solved “quadratic equations” when we set a polynomial equation equal to 0 Example. x 2 + 5x + 6 = 0.

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.

 Quadratic Equations Solve by Completing the Square.

I can solve one-step equations in one variable.. Equations that have the same solutions. In order to solve a one-step equation, you can use the properties.

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

Solving Quadratic Equations. Review of Solving Quadratic Equations ax 2 +bx +c = 0 When the equation is equal to zero, solve by factoring if you can.

8-1 Completing the Square

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,

WARM UP Find the product. 1.) (m – 8)(m – 9) 2.) (z + 6)(z – 10) 3.) (y + 20)(y – 20)

5.3 Solving Quadratic Functions with Square Roots Step 1: Add or subtract constant to both sides. Step 2: Divide or multiply coefficient of “x” to both.

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

Why we complete the square  We have learned how to factor quadratic expressions to solve.  Many quadratic equations contain expressions that cannot be.

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 1.) What is the graph of the function y = -x 2 + 4x + 1?

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

Notes Over 10.7 Factoring Special Products Difference of Two Squares.

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

Factor: 1. 2x 2 – 3x x 2 - 8x x 2 – 10x – 20.

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.

2.4 Quadratic Equations – Factoring & Completing the Square.

Then/Now You solved quadratic equations by using the square root property. Complete the square to write perfect square trinomials. Solve quadratic equations.

Solve Quadratic Functions by Completing the Square

Aim: How do we solve quadratic equations by completing square?

3.7 Completing the Square Objective:

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

Completing the Square, Quadratic Formula

Solve Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

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

Aim: How do we solve quadratic equations by completing square?

Solving Quadratic Equations by the Complete the Square Method

5.5 Completing the Square.

9.3 Solving Quadratic Equations

Section 11.2 The Quadratic Formula.

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.

9.3 Solve Quadratics by Completing the Square

1B.1- Solving Quadratics:

Special Problems (Solve)

Section 9.4 Day 1 Solving Quadratic Equations by Completing the Square

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.

Algebra 12.4 Completing the Square.

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

Solving Quadratics Using Square Roots

Section 9.4 Day 1 Solving Quadratic Equations by Completing the Square

9.2 Solving Quadratic Equations using square roots

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.

Simplify Radicals.

Completing the Square Algebra Review.

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.

Exercise Solve and check x – 3 = 5. x = 8 8 – 3 = 5.

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

Solving Quadratic Equations by Finding Square Roots

6-3 Completing the Square

Complete the Square January 16, 2017.

Presentation transcript:

5.6.2 – Solving Quadratics with Square Roots

Yesterday, we looked at the properties of square roots 1) Multiplication Property 2) Division Property 3) Simplifying square roots (pull out perfect roots)

Using Square Roots In some cases, we may use square roots to solve quadratics Must be a special case for us to use said method When can we use square roots? ax 2 – c = 0 (only for today)

Solving the Square Root Problem To solve the square root problem, all we will need to do is isolate the x 2 term, then take the square root of both sides Example. x 2 = 9 How would you “undo” the squared portion?

Example. Solve x 2 = 200 Example. Solve 2x 2 = 50

Example. Solve the quadratic x 2 – 18 = 0 How would you isolate the x 2 portion?

Example. Solve the quadratic 3x 2 – 60 = 0

Example. Solve the quadratic 2(x – 4) 2 = 10

Complete the following 4 problems together. You have 8 minutes. 1) x 2 = 49 2) 3x 2 – 1 = 14 3) 3x = 14 4) 2(x – 5) 2 = 12

Assignment Pg even