1. Section 4.6 – Completing the Square Students will be able to: To solve equations by completing the square To rewrite functions by completing the square Lesson Vocabulary: Completing the Square

2. Section 4.6 – Completing the Square

3. Forming a square with model pieces provides a useful geometric image for completing the square algebraically. Essential Understanding: Completing a perfect square trinomial allows you to factor the completed trinomial as the square of a binomial.

4. Section 4.6 – Completing the Square Problem 1: What is the solution of each equation? 4x 2 + 10 = 46

5. Section 4.6 – Completing the Square Problem 1: What is the solution of each equation? 3x 2 – 5 = 25

6. Section 4.6 – Completing the Square Problem 1: What is the solution of each equation? 7x 2 – 10 = 25

7. Section 4.6 – Completing the Square Problem 1: What is the solution of each equation? 2x 2 + 9 = 13

8. Section 4.6 – Completing the Square Problem 2: While designing a house, an architect used windows like the one shown here. What are the dimensions of the window if it has 2766 square inches of glass?

9. Section 4.6 – Completing the Square Problem 3: What is the solution of x 2 + 4x + 4 = 25?

10. Section 4.6 – Completing the Square Problem 3: What is the solution of x 2 – 14x + 49 = 25?

11. Section 4.6 – Completing the Square If x 2 + bx is not part of a perfect square trinomial, you can use the coefficient b to find a constant c so that x 2 + bx + c is a perfect square. When you do this, you are completing the square.

12. Section 4.6 – Completing the Square When you do this, you are completing the square.

13. Section 4.6 – Completing the Square When you do this, you are completing the square.

14. Section 4.6 – Completing the Square Problem 4: What value completes the square for x 2 – 10x? Justify your answer.

15. Section 4.6 – Completing the Square Problem 4: What value completes the square for x 2 + 6x? Justify your answer.

16. Section 4.6 – Completing the Square

17. Problem 5: What is the solution of 3x 2 – 12x + 6 = 0?

18. Section 4.6 – Completing the Square Problem 5: What is the solution of 2x 2 – x + 3 = x + 9?

19. Section 4.6 – Completing the Square You can complete a square to change a quadratic function to vertex form. Problem 6: What is y = x 2 + 4x – 6 in vertex form? Name the vertex and y-intercept.

20. Section 4.6 – Completing the Square Problem 6: What is y = x 2 + 3x – 6 in vertex form? Name the vertex and y-intercept.

21. Section 4.6 – Completing the Square Problem 6: What is y = 2x 2 – 6x – 1 in vertex form? Name the vertex and y-intercept.

22. Section 4.6 – Completing the Square Problem 6: What is y = -x 2 + 4x – 1 in vertex form? Name the vertex and y-intercept.

23. Section 4.6 – Completing the Square EXTRA PROBLEMS: Solve the quadratic by completing the square: x 2 – x = 5

24. Section 4.6 – Completing the Square EXTRA PROBLEMS: Solve the quadratic by completing the square: 2x 2 – ½x = 1/8

25. Section 4.6 – Completing the Square EXTRA PROBLEMS: Solve the quadratic by completing the square: 3x 2 +x = 2/3

26. Section 4.6 – Completing the Square EXTRA PROBLEMS: Solve the quadratic by completing the square: -.25x 2 – 0.6x + 0.3 = 0

27. Section 4.6 – Completing the Square EXTRA PROBLEMS: Solve for x in terms of a: 2x 2 – ax = 6a 2

28. Section 4.6 – Completing the Square EXTRA PROBLEMS: Solve for x in terms of a: 6a 2 x 2 – 11ax = 10

29. Section 4.6 – Completing the Square EXTRA PROBLEMS: Solve for x in terms of a: 4a 2 x 2 + 8ax + 3= 0

30. Section 4.6 – Completing the Square EXTRA PROBLEMS: Solve for x in terms of a: 4a 2 x 2 + 8ax + 3= 0

31. Section 4.6 – Completing the Square