1. Splash Screen

2. Lesson Menu Five-Minute Check (over Lesson 4–4) CCSS Then/Now New Vocabulary Example 1:Equation with Rational Roots Example 2:Equation with Irrational Roots Key Concept: Completing the Square Example 3:Complete the Square Example 4:Solve an Equation by Completing the Square Example 5:Equation with a ≠ 1 Example 6:Equation with Imaginary Solutions

3. Over Lesson 4–4 5-Minute Check 1 Simplify (5 + 7i) – (–3 + 2i). Solve 7x 2 + 63 = 0. What are the values of x and y when (4 + 2i) – (x + yi) = (2 + 5i)?

4. Over Lesson 4–4 5-Minute Check 1 A.5 B. C. D.

5. Over Lesson 4–4 5-Minute Check 2 A. B. C. D.

6. Over Lesson 4–4 5-Minute Check 3 A.2 + 9i B.8 + 5i C.2 – 9i D.–8 – 5i Simplify (5 + 7i) – (–3 + 2i).

7. Over Lesson 4–4 5-Minute Check 4 A.± 5i B.± 3i C.± 3 D.± 3i – 3 Solve 7x 2 + 63 = 0.

8. Over Lesson 4–4 5-Minute Check 5 A.x = 6, y = –7 B.x = –6, y = 7 C.x = –2, y = 3 D.x = 2, y = –3 What are the values of x and y when (4 + 2i) – (x + yi) = (2 + 5i)?

9. CCSS Content Standards N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. F.IF.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Mathematical Practices 7 Look for and make use of structure.

10. Then/Now You factored perfect square trinomials. Solve quadratic equations by using the Square Root Property. Solve quadratic equations by completing the square.

11. Vocabulary completing the square

12. Example 1 Equation with Rational Roots Solve x 2 + 14x + 49 = 64 by using the Square Root Property. x = 1 x = –15 Answer: The solution set is {–15, 1}. x = –7 + 8 or x = –7 – 8

13. Example 1 A.{–1, 9} B.{11, 21} C.{3, 13} D.{–13, –3} Solve x 2 – 16x + 64 = 25 by using the Square Root Property.

14. Example 2 Equation with Irrational Roots Solve x 2 – 4x + 4 = 13 by using the Square Root Property.

15. Example 2 Solve x 2 – 4x + 4 = 8 by using the Square Root Property. A. B. C. D.

16. Concept

17. Example 3 Complete the Square Find the value of c that makes x 2 + 12x + c a perfect square. Then write the trinomial as a perfect square. Step 1 Answer: The trinomial x 2 + 12x + 36 can be written as (x + 6) 2. Step 26 2 = 36 Step 3Add the result of Step 2 to x 2 + 12x + 36 x 2 + 12x.

18. Example 3 A.9; (x + 3) 2 B.36; (x + 6) 2 C.9; (x – 3) 2 D.36; (x – 6) 2 Find the value of c that makes x 2 + 6x + c a perfect square. Then write the trinomial as a perfect square.

19. Example 4 Solve an Equation by Completing the Square Solve x 2 + 4x – 12 = 0 by completing the square. x 2 + 4x – 12=0 x 2 + 4x=12 (x + 2) 2 =16 x + 2= ± 4 Answer: The solution set is {–6, 2}. x=– 2 ± 4 x = –2 + 4 or x = –2 – 4 x = 2 x = –6

20. Example 4 Solve x 2 + 6x + 8 = 0 by completing the square. A. B. C. D.

21. Example 5 Equation with a ≠ 1 Solve 3x 2 – 2x – 1 = 0 by completing the square. 3x 2 – 2x – 1=0

22. Example 5 Solve 2x 2 + 11x + 15 = 0 by completing the square. A. B. C. D.

23. Example 6 Equation with Imaginary Solutions Solve x 2 + 4x + 11 = 0 by completing the square.

24. Example 6 Solve x 2 + 4x + 5 = 0 by completing the square. A. B. C. D.

25. End of the Lesson