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# 5.7 c - each 12 2 =-x x Step 6 Solve for x You try 4 4 2 =...

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1 5.7 Notes Completing the Square Warm-up: 1) 2) Factor this perfect square trinomial. 3) ) 3 )( 3 ( - - x x 4 - ± 36 12 2 + - x x Objective: - solve equations by completing the square -rewrite functions by completing the square Solving Perfect Square Trinomial Equations Solve: Step 1: Factor the trinomial Step 2: Find the square root of each side Step 3: Solve for x. 36 25 10 2 = + + x x Completing the Square If one side of an equation is not a perfect square trinomial, you can convert it into one by rewriting the constant term. Perfect Square Trinomial: 2 2 2 + + b bx x Use this to find the missing value for c. Examples: 1) 2) _____ 8 2 + - x x _____ 7 2 + + x x Completing the Square You can solve ANY quadratic equation by completing the square. Step 1: Subtract 5 from both sides 0 5 12 2 = + - x x Step 2: Find Step 3: Complete the square by adding that value to both sides. 2 2 b Completing the Square Step 4: Factor the perfect square trinomial Step 5: Find the square root of

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Unformatted text preview: each side 31 36 12 2 = +-x x Step 6: Solve for x. You try! 4 4 2 =-+ x x 1) 2) 1 2 2 =--x x 2 Finding Complex Solutions Solve. * fol ow same steps, but the last step wil cause you to have a complex number solution. 36 8 2 = +-x x Try solving on a graphing calculator. What happens? Finding Complex Solutions c When the quadratic term has a coefficient that is not 1, you can stil solve by completing the square. Step 1: Divide each side by the coefficient. 8 6 5 2 + = x x You try! 1) 4 3 2 2-= x x Converting from Standard to Vertex Form by Completing the Square. c bx ax y + + = 2 k h x a y +-= 2 ) ( 2 6 2 + + = x x y b Step 1: Add and subtract to the right side. Step 2: Factor the perfect square trinomial. 2 2 b Step 3: Simplify Homework: p. 281 # 1-3, 7-9, 13-18, 28, 30...
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5.7 c - each 12 2 =-x x Step 6 Solve for x You try 4 4 2 =...

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