1. Opener-SAME SHEET-9/21 Find vertex and describe transformation
F(x) = 3(x +2) b. f(x) = -(x)2 + 7
2. Find vertex f(x) = -3x2 + 6x
3. Solve by factoring.
a.x = 12x b. 0= x2 – 8x + 12

2. Factor Practice
X2 – 7x -30=0
X2 + 4x – 32=0

3. Solve using square roots
HW Quiz 9-7(Square Root)
Solve using square roots
20x2 = 500
X2 = - 400
36x2 = 100
4x = 80

4. 9-8 Completing the Square Warm Up Lesson Presentation Lesson Quiz
Holt Algebra 1

5. Find four numbers that make this factorable.
x2 + 8x + ____

7. Objective
Solve quadratic equations by completing the square.

8. Vocabulary
completing the square

9. Opener-SAME SHEET-9/22 Solve by finding square root. 49x2 + 1 = 170
Solve by factoring
3. -2x2 = 18 – 12x

10. In the previous lesson, you solved quadratic equations by isolating x2 and then using square roots. This method works if the quadratic equation, when written in standard form, is a perfect square.
When a trinomial is a perfect square, there is a relationship between the coefficient of the x-term and the constant term.
X2 + 6x x2 – 8x + 16

11. An expression in the form x2 + bx is not a perfect square
An expression in the form x2 + bx is not a perfect square. However, you can use the relationship shown above to add a term to x2 + bx to form a trinomial that is a perfect square. This is called completing the square.

12. Example 1: Completing the Square
Complete the square to form a perfect square trinomial.
A. x2 + 2x +
B. x2 – 6x +

13. Check It Out! Example 1
Complete the square to form a perfect square trinomial.
a. x2 + 12x +
b. x2 – 5x +

14. To solve a quadratic equation in the form x2 + bx = c, first complete the square of x2 + bx. Then you can solve using square roots.

15. Reading Strategies Wkst
Solving a Quadratic Equation by Completing the Square
Reading Strategies Wkst

18. Example 2B: Solving x2 +bx = c
Solve by completing the square.
x2 – 4x – 6 = 0
x = 2 + √10 or x = 2 – √10

20. Partners

21. Opener-SAME SHEET-9/22 1. Solve by completing the square
x2 - 10x + 24 = 0

22. Opener-SAME SHEET-9/23 Solve by graphing x2 + 5 = 6x b. x2 + 8x +12=0
2. Solve by factoring
x2 -2x – 15 = 0 b. x2 + 9x = -14
3. Solve by Sq. Root
a. 5x2 = b. x2 = -16

23. Check It Out! Example 2b
Solve by completing the square.
t2 – 8t – 5 = 0
Step 6 t = 4 + √21 or t = 4 – √21

24. Finish Signs

25. Wkst

26. Signs x2 - 10x + 24 = 0 x2 - 6x = –9 2x2 + 14x = 16 x2 + 14x + –26 = 0

27. #7 Type 2 Name
What does it mean to solve a quadratic equation? Describe how to solve the quadratic equation by completing the square. Use this example to help you explain.
X2 + 14x = 15
SKIP LINES

28. Example 4: Problem-Solving Application
A rectangular room has an area of 195 square feet. Its width is 2 feet shorter than its length. Find the dimensions of the room. Round to the nearest hundredth of a foot, if necessary.

29. Example 4 Continued
x = 13 or x = –15

30. Check It Out! Example 4
An architect designs a rectangular room with an area of 400 ft2. The length is to be 8 ft longer than the width. Find the dimensions of the room. Round your answers to the nearest tenth of a foot.

31. Check It Out! Example 4 Continued
x  16.4 or x  –24.4

32. Lesson Quiz: Part I
Complete the square to form a perfect square trinomial.
1. x2 +11x +
2. x2 – 18x +
Solve by completing the square.
3. x2 – 2x – 1 = 0
4. 3x2 + 6x = 144
5. 4x x = 23 81
6, –8

33. Lesson Quiz: Part II
6. Dymond is painting a rectangular banner for a football game. She has enough paint to cover 120 ft2. She wants the length of the banner to be 7 ft longer than the width. What dimensions should Dymond use for the banner?
8 feet by 15 feet