1 / 8

M ODELING C OMPLETING THE S QUARE

x. x. x. x. x. x. x 2. x. x. x. M ODELING C OMPLETING THE S QUARE. Use algebra tiles to complete a perfect square trinomial. Model the expression x 2 + 6 x. Arrange the x -tiles to form part of a square. 1. 1. 1. 1. 1. 1. To complete the square, add nine 1-tiles. 1. 1.

tehya
Télécharger la présentation

M ODELING C OMPLETING THE S QUARE

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. x x x x x x x2 x x x MODELING COMPLETING THE SQUARE Use algebra tiles to complete a perfect square trinomial. Model the expression x2 + 6x. Arrange the x-tiles to form part of a square. 1 1 1 1 1 1 To complete the square, add nine 1-tiles. 1 1 1 x2 + 6x + 9 = (x + 3)2 You have completed the square.

  2. SOLVING BY COMPLETING THE SQUARE 2 2 ) ( ) ( b b x2 + bx + = x + 2 2 To complete the square of the expressionx2 + bx, add the square of half the coefficient ofx.

  3. Completing the Square 2 ( ) –8 The coefficient of x is –8, so you should add , or 16, to the expression. 2 2 ( ) –8 x2 – 8x + = x2 – 8x + 16 = (x – 4)2 2 What term should you add tox2 – 8xso that the result is a perfect square? SOLUTION

  4. Completing the Square 1 x2 – x = 1 2 2 2 ( 2 ) ( ) 1 1 1 1 ( ) 1 1 1 – – Add = , or x2–x+ = 1 + – • 2 16 2 2 4 16 4 to each side. Factor2x2 – x – 2 = 0 SOLUTION 2x2 – x – 2 = 0 Write original equation. 2x2 – x = 2 Add 2 to each side. Divide each side by 2.

  5. Completing the Square 2 ( ) 1 1 x2–x+ = 1 + – 16 1 4 2 2 ( ) 1 17 = x – 16 4 1 17 17 17 17 x – = ± 4 4 4 4 4 1 1 x = ± Add to each side. 4 2 2 4 ( ) ( ) 1 1 1 1 – – Add = , or • 2 16 2 4 to each side. 1 1 – The solutions are +  1.28 and  – 0.78. 4 4 Write left side as a fraction. Find the square root of each side.

  6. Completing the Square 17 17 4 4 CHECK 1 1 – The solutions are +  1.28 and  – 0.78. 4 4 You can check the solutions on a graphing calculator.

  7. Perform the following steps on the general quadratic equation ax2 + bx + c = 0 where a 0. –c bx x2+ + = a a ( ) ( ) bx –c b b 2 2 x2+ + = + a a 2a 2a ( ) b –c b2 2 x + = + a 2a 4a2 ( ) –4ac + b2 b 2 x + = 4a2 2a CHOOSING A SOLUTION METHOD Investigating the Quadratic Formula ax2 + bx = –c Subtractcfrom each side. Divide each side bya. Add the square of half the coefficient ofxto each side. Write the left side as a perfect square. Use a common denominator to express the right side as a single fraction.

  8. ( ) b –4ac + b2 2 Use a common denominator to express the right side as a single fraction. x + = 2a 4a2 2 ± - b b 4 ac 2 ± - x + = b 4 ac 2a 2a 2a b x= – 2a 2 ± - b 4 ac –b x= 2a CHOOSING A SOLUTION METHOD Investigating the Quadratic Formula Find the square root of each side.Include±on the right side. Solve for x by subtracting the same term from each side. Use a common denominator to express the right side as a single fraction.

More Related