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Published byMollie Gradin Modified over 2 years ago

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Todays Objectives: Todays Agenda SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics Homework #11: Pg 124 #35 - 56 Todays Vocabulary: Square Square root Radical

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Solving Quadratic Equations by Completing the Square

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Perfect Square Trinomials l Examples l x 2 + 6x + 9 l x 2 - 10x + 25 l x 2 + 12x + 36 SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Creating a Perfect Square Trinomial l In the following perfect square trinomial, the constant term is missing. X 2 + 14x + ____ l Find the constant term by squaring half the coefficient of the linear term. (14/2) 2 = 7 2 = 49 X 2 + 14x + 49 SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Perfect Square Trinomials l Create perfect square trinomials l x 2 + 20x + ___ l x 2 - 4x + ___ l x 2 + 5x + ___ SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation. SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Solving Quadratic Equations by Completing the Square If you want the vertex form of the equation you are almost there: (x-4) 2 = 36 can be converted into vertex form by subtracting 36 from both sides. So you get: (x-4) 2 – 36 = 0 with vertex (4, -36) SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side To find the roots of the equation: SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilitie s and solve So your two roots written as x-intercepts are: (-10, 0) and (2,0) SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Completing the Square-Example #2 Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation, the constant to the right side of the equation. SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. Step 3 : Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation. (x + 1) 2 = 64 SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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Solving Quadratic Equations by Completing the Square 1. x 2 + 8x - 84 = 0 2. x 2 – 5x - 24 = 0 x = 6, x = -14 x = -3, x = 8 Try the following examples. Do your work on your paper and then check your answers. SWBAT… Rewrite Standard form equations in Vertex form Apply complete the square technique to Standard form equations Understand that completing the square is another way to find solutions to quadratics

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