Completing the Square

1. Completing the Square Slideshow 20 Mathematics Mr SasakiRoom 307

2. Objectives • Practice solving equations in the form • Solve quadratic equations by completing the square where there is an even coefficient of • Solve quadratic equations by completing the square where there is an odd coefficient of

3. Solving Equations Let’s have a bit of a warm up. No challenge here! Example Solve . Let’s try the first worksheet!

5. Completing the Square We did this in Grade 8! We need to transform one side of the equation to make a perfect square. Example Write what you need to add to make a perfect square for… These values are half of the -coefficients. We half and square the coefficient. How do they factorise?

6. Completing the Square We can use this concept to write some quadratic equation in the form where . Example By completing the square, solve . Note: We must write it in the form . or

7. Completing the Square Let’s try another example. Example By completing the square, solve .

8. or or or or

9. Completing the Square Working with odd numbers makes things messier. Example By completing the square, solve . or

10. or or or or

11. or or or or (both negative roots) or (positive) or (positive)