PPT-9.4 Solve by Completing the Square

What We Will Learn Complete the square Solve by completing the square Needed Vocab Completing the square adding a constant to an expression to turn into a perfect square trinomial Ex 1 Completing the Square. This PowerPoint . was adapted from . http://. www.purplemath.com/modules/quadform2.htm. and . http://. teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/6-4/2006_6_4.ppt. Looking Back…. In our previous lesson, we solved quadratic function by . Lesson 5.6. Warm-up. Solve:. 2. Simplify:. . Solving Quadratic Equations: Sometimes you can use square roots to solve some quadratic equations. However, you must remember that. so you must have both the positive and negative value for your answer.. Section 3.3 Beginning on page 112. The Big Idea. Completing the square . is a technique we can use to write a quadratic in vertex form.. Completing the square is creating a . Perfect Square Trinomial. Mary has (4x +10) dollars and Ron has (-5x + 20) dollars. How much more money does Mary have than Ron?. The measure of the perimeter of a triangle is (37m+42). It is known that two of the sides of the triangle have measures of (14m +16) and (10m +20). Find the length of the third side. . Perfect Square Trinomials. Examples. x. 2. + 6x + 9. x. 2. - 10x + 25. x. 2. + 12x + 36. Creating a Perfect . Square Trinomial. X. 2. . + 14x + ____ . Find the constant term by squaring half . Find the roots:. 1) x. 2. – 64 = 0 . 2) 8x. 2. – 64x = 0. 3) x. 2. – 16x + 64 = 0. 1) Ensure the quadratic equation is set to zero.. 2) Factor the quadratic equation (GCF, perfect square binomial [DOTS], trinomial). ?. What is optimization?. Some of the most important applications of differential calculus are optimization problems, in which we are required to find the optimal (best) way of doing something. Many practical problems require us to minimize a cost or maximize an area or somehow find the best possible outcome of a situation.. Objective: To complete a square for a quadratic equation and solve by completing the square. Steps to complete the square. 1.) You will get an expression that looks like this: . . . AX. ² BX. Mathematics. Mr Richard Sasaki, Room 307. Recall how to solve quadratic equations through factorisation. Learn how to “complete the square” to solve equations for . ..  . Objectives. As we learned last class, to factorise a quadratic equation, we look for two numbers that add together to make the . You have learned three methods for solving equations of the form. When . , you can solve by using the square root property. For example: . If the expression . is factorable, then you can use the Product Property of Zero. Completing the Square with Algebra Tiles. Completing the Square. 2. Algebra tiles can be used to complete the . square. Use . tiles and frame to represent problem. . The expression . should form a . I can find zeros by completing the square. Warm Up. Rewrite the following as perfect squares.. 1. x. 2. 14x 49 . ( _______). 2. 2. x. 2. -2x 1. (________). 2. Our goal. What if you were asked to complete the pattern of a perfect square.. GCSE: Solving Quadratic Equations Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2 nd June 2015 Overview There are 4 ways in which we can solve quadratic equations.   1 By Factorising 2 Take out: . HW. Packet. Quiz from . fri. . SWBAT: Solving quadratics by completing the square . -8. -8. 2(x-2). 2. = -12. 2. 2. (x-2). 2. = -6.  . x-2 = ±. i.  . +2. +2. x = 2 ± . i.  . SWBAT: Solving quadratics by completing the square .