factoring x 2 = 9 x 2 - 9 = 0 (x + 3)(x - 3) = 0 x + 3 = 0 or x - 3 = 0 x = -3 or x = 3 x = {-3, 3}...

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  • Slide 1
  • Factoring x 2 = 9 x 2 - 9 = 0 (x + 3)(x - 3) = 0 x + 3 = 0 or x - 3 = 0 x = -3 or x = 3 x = {-3, 3} Zero-factor property
  • Slide 2
  • Another Way to Solve Quadratics Square Root Property When you introduce the radical you must use + and - signs. Recall that we know the solution set is x = {-3, 3}
  • Slide 3
  • 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
  • Slide 4
  • Perfect Square Trinomials l Create perfect square trinomials. l x 2 + 20x + ___ l x 2 - 4x + ___ l x 2 + 5x + ___ 100 4 25/4
  • Slide 5
  • 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. l (14/2) 2 X 2 + 14x + 49
  • Slide 6
  • 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.
  • Slide 7
  • Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side
  • Slide 8
  • Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve
  • Slide 9
  • Solving Quadratic Equations by Completing the Square
  • Slide 10
  • Section 8.1 Completing the Square
  • Slide 11
  • Factoring Before today the only way we had for solving quadratics was to factor. x 2 - 2x - 15 = 0 (x + 3)(x - 5) = 0 x + 3 = 0 or x - 5 = 0 x = -3 or x = 5 x = {-3, 5} Zero-factor property
  • Slide 12
  • Square Root Property If x and b are complex numbers and if x 2 = b, then OR
  • Slide 13
  • Solve each equation. Write radicals in simplified form. Square Root Property
  • Slide 14
  • Solve each equation. Write radicals in simplified form. Square Root Property Radical will not simplify.
  • Slide 15
  • AAT-A Date: 2/5/14 SWBAT complete the square to solve factoring problems Do Now: HW Requests: pg 303 #42-49; Pg 310 #15-37 odds In Class: Start Completing the Square WS HW: Complete WS KutaSoftware 1-24 odds Begin Section 6.5 Announcements: Tutoring: Tues. and Thurs. 3-4 Bring Graphing Calculator to Class for Thursday Quiz Friday w/HW Quiz before Complete presentations Life Is Just A Minute Life is just a minuteonly sixty seconds in it. Forced upon youcan't refuse it. Didn't seek itdidn't choose it. But it's up to you to use it. You must suffer if you lose it. Give an account if you abuse it. Just a tiny, little minute, But eternity is in it! By Dr. Benjamin Elijah Mays, Past President of Morehouse College
  • Slide 16
  • Solve each equation by factoring. 3x 2 =5x Homework Quiz
  • Slide 17
  • Solve each equation by factoring. 3x 2 =5x x= {0, 5/3} Homework Quiz
  • Slide 18
  • Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers.
  • Slide 19
  • Solve each equation. Write radicals in simplified form. Solution Set Square Root Property
  • Slide 20
  • Solve each equation. Write radicals in simplified form.
  • Slide 21
  • Slide 22
  • Perfect Square Trinomials l Examples l x 2 + 6x + 9 l x 2 - 10x + 25 l x 2 + 12x + 36
  • Slide 23
  • Completing the Square 1. Divide by the coefficient of the squared term. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve.
  • Slide 24
  • Completing the Square 1.Divide by the coefficient of the squared term. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve.
  • Slide 25
  • Completing the Square 1. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve.
  • Slide 26
  • Completing the Square 1.Divide by the coefficient of the squared term. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve.
  • Slide 27
  • 1. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve.
  • Slide 28
  • Solving Quadratic Equations by Completing the Square x 2 - 2x - 15 = 0 (x + 3)(x - 5) = 0 x + 3 = 0 or x - 5 = 0 x = -3 or x = 5 x = {-3, 5} Now take 1/2 of the coefficient of x. Square it. Add the result to both sides. Factor the left. Simplify the right. Square Root Property
  • Slide 29
  • 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.
  • Slide 30
  • Deriving The Quadratic Formula Divide both sides by a Complete the square by adding (b/2a) 2 to both sides Factor (left) and find LCD (right) Combine fractions and take the square root of both sides Subtract b/2a and simplify
  • Slide 31
  • 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.
  • Slide 32
  • 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. The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient first.
  • Slide 33
  • 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.
  • Slide 34
  • Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

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