PPT-Solving Quadratic Equations by Completing the Square

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 . Steps for solving a quadratic equation by completing the square 1 Isolate the constant on one side 2 Make sure that the coe64259cient in front of the squared term is a positive one If it is not divide every term of the equation by this coe64259cient Grades C to A*. Hyperlinks!. Expanding a single bracket. Solving quadratics by factorising. Factorising quadratic expressions. Factoring expressions. Multiplying out 2 brackets. Quadratic simultaneous equations. 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. . Solve:. LINEAR . QUADRATIC . QUADRATIC . Quadratic Equations. Solve:. a) b) . . Learning Log Summary . LT. . 1. . – I can . solve. quadratic equations using factoring or the square root method.. Mathematical Language. A . solution. of an equation is a number that make the equation true. 3x+2=17. To . solve. an equation means to find all its solution. Two equations are equivalent if they have the same solutions. Standards 8-10. Graphs of Quadratic Functions . U- Shaped Graph . Vertical y=x. 2. or Horizontal x=y. 2. Positive Negative . Summary: The of a Quadratic Function is U shaped. . Positve. Expanding. Brackets. Factorising. Expanding . Double . Brackets. Solving . Linear . Equations. Plotting graphs by. substitution into . equations. Solving . Quadratic. Equations. Solving . Quadratics. In preparation for the Algebra CST. -b . . b. 2. – 4ac. 2ac. √. (x 4)(x-3)=0. (x 1)(x 2). X. 2. – 5x 4. F O I L. Complete. The Square. Multiplying Polynomials. Area Model of Multiplication. 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. 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. 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