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Tuesday: Announcements Upcoming Retest Extra Credit Available

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Re-testing Unit 5 TUTORIALSTuesdayWednesdayThursdayFriday Morning 7:45am YES NOYES Afternoon 3:55 pm YESNOYESNO

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Thanksgiving Extra Credit Loaded on website on Friday after school DUE before 1 st period (8:35am) on Monday 12-2-13. Will not accept late!. See me if this is not possible. Earn up to 8 points on Test Grade based on what you get correct. Must do the entire review to be scored, not just parts. Must show work to get credit, unless problem says no work required (NW)

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Warm-up Convert to Vertex Format by Completing the Square y = 3x 2 + 18x + 20

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Chapter 4 Section 4-7 Solving by Completing the Square

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Objectives I can find the solutions to a quadratic equation by completing the square

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Solving by Completing the Square Given a quadratic equation ax 2 + bx + c = 0 Step 1: Move number to Right Side of Equation if necessary Step 2: Make the Left side a Perfect Square Step 3: Solve using Square Roots Method learned earlier this unit

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Solving by Taking Square Root x 2 – 6x + 9 = 25 (x –3)(x – 3) = 25 (x - 3) 2 = 25 x – 3 = +/- 5 x = 3 +/- 5 x = 8 or –2 {-2, 8}

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Teeter-Toter Keeping Balanced +20

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Example 1 x 2 – 6x – 40 = 0 x 2 – 6x = 40 x 2 – 6x + _____ = 40 + _____ x 2 – 6x + 9 = 40 + 9 (x – 3) 2 = 49 x – 3 = x = 3 7 x = 10 or -4

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Example 2 x 2 + 8x + 20 = 0 x 2 + 8x = -20 x 2 + 8x + ____ = -20 + ____ x 2 + 8x + 16 = -20 + 16 (x + 4) 2 = -4 x + 4 = x = -4 2i

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GUIDED PRACTICE for Examples 3, 4 and 5 Solve x 2 + 6x + 4 = 0 by completing the square. x 2 + 6x + 4 = 0 Write original equation. x 2 + 6x = – 4 Write left side in the form x 2 + bx. x 2 + 6x + 9 = – 4 + 9 Add 6 2 2 ( ) = (3) 2 = 9 to each side. (x + 3) 2 = 5 Write left side as a binomial squared. Solve for x. Take square roots of each side. x + 3 = + 5 x = – 3 + 5 The solutions are – 3+ and – 3 – 2 5 ANSWER 7.

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GUIDED PRACTICE for Examples 3, 4 and 5 Solve 3x 2 + 12n – 18 = 0 by completing the square. Write original equation. x 2 + 4n = 6 Write left side in the form x 2 + bx. x 2 + 4x + 4 = 6 + 4 Add 4 2 2 ( ) = (2) 2 = 4 to each side. (x + 2) 2 = 10 Write left side as a binomial squared. Solve for x. Take square roots of each side. x + 2 = + 10 x = – 2 + 10 10. 3x 2 + 12n – 18 = 0 Divided each side by the coefficient of x 2. x 2 + 4n – 6 = 0

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Homework WS 6-4

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Why we complete the square We have learned how to factor quadratic expressions to solve. Many quadratic equations contain expressions that cannot be.

Why we complete the square We have learned how to factor quadratic expressions to solve. Many quadratic equations contain expressions that cannot be.

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