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 . Quadratic Equations. Prepared by . Doron. . Shahar. Warm-up: page . 15. A . quadratic equation. is an equation that . can be. . written. in the form _____________ where . a. , . b. , and. c. are constants and . 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. Page 3. General equation of a quadratic:. Quadratic Formula:. Notice where the letters come from for the formula. We use the quadratic formula when something can not be factored. However, it also works for factorable quadratic equations as well.. 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.. If you read from left to right . 10 . “is greater than “ . 5. . X. If you read from right to left . 5. . “is less than “ . 10. . X. If you read from left to right . 5. . “is less than “ . Problem 1. There are 25 toys in a playground. . The toys are either bicycles (2 wheels) or tricycles (3 wheels). . In total in the playground there are 61 wheels. . How many bicycles are in the playground?. 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. If you read from left to right . 10 . “is greater than “ . 5. . X. If you read from right to left . 5. . “is less than “ . 10. . X. If you read from left to right . 5. . “is less than “ . 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. 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.. 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. Recall, we went over how to factor quadratics that are trinomials. Example. Factor the expression x. 2. 7x 12. Quadratic Equations. Quadratic Equations. are written in the form ax. 2. . bx. c = 0. 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 . 1North Carolina Standard Course of StudyNorth Carolina Math 2Standards for Mathematical Practice1Make sense of problems and persevere in solving them2Reason abstractly and quantitatively3Construct via