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An introductory lesson on completing the square

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- 1. Try to factorise each of these two expressions before the music ends. What do you notice? HINT: Mr Lock is not being very nice again! x ² + 8x + 15 x ² + 2x - 5 Check with the person next to you that they did it the same way as you. Extension: can you solve x ² + 8x + 15= 0 or x ² + 2x - 5= 0
- 2. The Big Picture You have: Rearranged expressions and equations Solved complex equations Solved quadratic equations Factorised quadratics Used the common factor Manipulated algebra Now we’re going to go a step further with quadratic expressions and do something called ‘completing the square’, using all the above
- 3. x ² + 8x + 15 = 0 x ² + 2x – 5 = 0 Recap (x+5)(x+3) = 0 x+5 = 0 or x+3 = 0 X= -5 or x = -3 ?
- 4. Learning Objectives : To solve quadratic equations by factorising and by completing the square Outcomes: To be successful, you will have solved at least one by factorising (C) and one quadratic expression using the completing the square method (A) This means by the end of the lesson you will be able to solve that second question from your bell work
- 5. Do this one in 90 seconds… Find x… x ² + 6x + 8 = 0
- 6. Multiply out (x+3) ² (x+3) ² = x² + 6x + 9 Notice for today’s lesson that this 9 is the same as 3 ² Now we’re going to use this to solve x ²+6x -12 = 0
- 7. You try: x ²+ 4x – 20 = 0 If finished, do some of Exercise 30B (page 489) while waiting.
- 8. <ul><li>Mr Lock’s quick guide (do not write this down) </li></ul><ul><li>1) Half the middle term and make a ‘square’. </li></ul><ul><li>2) Make sure the equation is balanced (ie complete the square). </li></ul><ul><li>3) Put the ‘square’ on one side and the rest on the other. </li></ul><ul><li>4) Square root to solve in surd form </li></ul><ul><li>5) Use your calculator to get the decimal answer </li></ul>
- 9. <ul><li>Mr Lock’s quick guide (do not write this down) </li></ul><ul><li>1) Half the middle term and make a ‘square’. </li></ul><ul><li>2) Make sure the equation is balanced (ie complete the square). </li></ul><ul><li>3) Put the ‘square’ on one side and the rest on the other. </li></ul><ul><li>4) Square root to solve in surd form </li></ul><ul><li>5) Use your calculator to get the decimal answer </li></ul>Try these Activity x ²+6x -30 x²+4x-8 x²+16x-27 x²-10x-36 x²-3x-9
- 10. Textbook Now try exercise 30B Questions 1 and 2
- 11. Demonstrate Solve this equation giving your answer to 3 sf x ² + 2x – 5 = 0
- 12. Learning Objectives : To solve quadratic equations by factorising and by completing the square Outcomes: To be successful, you will have solved at least one by factorising (C) and one quadratic expression using the completing the square method (A) Review/ plenary What can you do now that you couldn’t do an hour ago (be specific)? Can you write down a ‘quick guide’ to completing the square, small enough for a revision card?
- 13. Home Learning Complete questions 1 & 2 and the crossword. Due Weds 24 th January 2007

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