Section 4.6 Completing the Square

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

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.

Completing the Square Perfect Square Trinomials: Factor: This is called a perfect square trinomial because the factors are the same. So we can rewrite.

Algebra Core Review Day 7

Factoring Polynomials by Completing the Square. Perfect Square Trinomials l Examples l x 2 + 6x + 9 l x x + 25 l x x + 36.

8-1 Completing the Square

Section 10.6 Factoring Objectives: Factor a quadratic expression of the form Solve quadratic equations by factoring.

Essential Question: How is the process of completing the square used to solve quadratic equations? Students will write a summary of how they use completing.

Solving Quadratic Equations by Completing the Square.

Solve a quadratic equation by finding square roots

Algebra Completing the Square. Solving with Square Roots.

Do Now Factor the expression. x2 + 18x + 81 x2 - 22x

Solve Quadratic Functions by Completing the Square

Chapter 4: Quadratic Functions and Equations

Solve Quadratic Equations by Completing the Square

Algebra 1 Warm up #3 Solve by factoring:.

Solving Quadratic Equations by Completing the Square

International Studies Charter School

Perfect Square Trinomials:

COMPLETING THE SQUARE.

Solving the Quadratic Equation 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.

Write each expression as a trinomial.

Solve a quadratic equation

4.6 Completing the Square Learning goals

4.6 Completing the Square Learning goals

Solving Quadratic Equations by Completing the Square

Completing the Square (3.2.3)

Algebra II Section 4.5a Complete the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

EXAMPLE 1 Complete the square

Solving Quadratic Equations by Completing the Square

SECTION 9-3 : SOLVING QUADRATIC EQUATIONS

Section 6.1 Simplifying Rational Expressions and NPV’s

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

9.3 Solve Quadratics by Completing the Square

Why Use “Completing the Square”

Solving Quadratic Equations by Completing the Square

Ch3/4 Lesson 7 Completing The Square

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.

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Quadratic Equations and Functions

Solving Quadratic Equations by Completing the Square

Section 9.4 Day 1 Solving 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.

Solving 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.

Solving Quadratic Equations by Completing the Square

Ch3/4 Lesson 1 Review on factoring trinomials

Solving 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.

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Complete the Square January 16, 2017.

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Presentation transcript:

Section 4.6 Completing the Square

Perfect Trinomials: When a perfect trinomial is factored, both binomials will be equal The third term in a perfect trinomial is equal to the second term divided by 2 and then squared The term in the binomial is equal to the second term divided by 2 When we CTS, we change the trinomial into a perfect trinomial © Copyright all rights reserved to Homework depot: www.BCMath.ca

What is “Completing the Square” “Completing the Square” is a process that converts a quadratic function that can not be factored to a form that can be solved algebraically Suppose we have the following trinomial If we complete the square, we end up with the expression on the right Can’t factor this… We end up with two answers in radical form

How to Complete the Square Bracket the first two terms! Divide the second term by 2 and square it! Purpose: Make the expression in the bracket into a perfect square! Take the negative square outside of the brackets! The trinomial becomes two equal binomials Now you can solve this equation by square rooting both sides:

Ex: Complete the Square and Solve for “x” Bracket the first two terms! Factor out any coefficient for x2 Divide the second term by 2 and square it! Take the negative square outside of the brackets and multiply with coefficient in front! The trinomial becomes two equal binomials Solve for “x” by square rooting both sides

Ex: Solve for “x” by Completing the Square:

Ex: The sum of two numbers is 80. Their product is 1500 Ex: The sum of two numbers is 80. Their product is 1500. Find the numbers There are two numbers, let ‘x’ and ‘y’ be the numbers Gather Information The sum is 80 The product is 1600 Substitute the first equation into the second one. The two numbers are 30 and 80

Ex: The difference of two numbers is 10. The sum of their squares is 60. Find the numbers There are two numbers, let ‘x’ and ‘y’ be the numbers Gather Information The difference is 10 The sum of their squares is 60 Substitute the first equation into the second one. The two sets of numbers are: