Opener-SAME SHEET-9/21 Find vertex and describe transformation F(x) = 3(x +2)2 b. f(x) = -(x)2 + 7 2. Find vertex f(x) = -3x2 + 6x 3. Solve by factoring. a.x2 + 36 = 12x b. 0= x2 – 8x + 12

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

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

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

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

Objective Solve quadratic equations by completing the square.

Vocabulary completing the square

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

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 + 9 x2 – 8x + 16

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.

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

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

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.

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

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

Partners

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

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 = 320 b. x2 = -16

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

Finish Signs

Wkst

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

#7 Type 2 Name 4-24-09 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

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.

Example 4 Continued x = 13 or x = –15

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.

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

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. 4x2 + 44x = 23 81 6, –8

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