1. Solve.

4. Question of the Day

5. CCGPS Geometry Day 62 (10-24-13) UNIT QUESTION: How are real life scenarios represented by quadratic functions? Today’s Question: When is it useful to solve quadratics by completing the square? Standard: MCC9-12..A.REI.4b

6. Completing the Square Completing the square is used for all those not factorable problems!! It is used to solve these equations for the variable. It gets a little messy when a is not 1.

7. Perfect Square Trinomials Examples l x 2 + 6x + 9 l x 2 - 10x + 25 l x 2 + 12x + 36

8. Creating a Perfect Square Trinomial l In the following perfect square trinomial, the constant term is missing. x 2 + 14x + ____ l Find the constant term by squaring half the coefficient of the linear term. l (14/2) 2 x 2 + 14x + 49

9. Perfect Square Trinomials Create perfect square trinomials. l x 2 + 20x + ___ l x 2 - 4x + ___ l x 2 + 5x + ___

10. Example 1 Solving by Completing the Square Solve the following equation by completing the square: Step 1: Rewrite so all terms containing x are on one side.

11. Example 1 Continued Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

12. Example 1 Continued Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation. Step 4: Take the square root of each side.

13. Example 1 Continued Step 5: Solve for x.

14. Example 2 Solving by Completing the Square Solve the following equation by completing the square: Step 1: Rewrite so all terms containing x are on one side.

15. Example 2 Continued Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

16. Example 2 Continued Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation. Step 4: Take the square root of each side.

17. Example 2 Continued Step 5: Solve for x.

18. Solve each by Completing the Square

19. x 2 + 4x – 4 = 0x 2 – 2x – 1 = 0

20. Example 4 Finding Complex Solutions x 2 - 8x + 36 = 0x 2 +6x = - 34

21. Example 5 Solving When a≠0