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Solving Quadratic Equations by Completing the Square

Learn how to solve quadratic equations by creating perfect square trinomials through completing the square method. Examples and step-by-step instructions provided.

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Solving Quadratic Equations by Completing the Square

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  1. Warm Up • Find the roots

  2. Solving Quadratic Equations by Completing the Square

  3. Objective: We are gong to create our own Perfect Square Trinomials. In order to solve quadratic equations more effectively. • Examples • x2 + 6x + 9 • x2 - 10x + 25 • x2 + 12x + 36

  4. Creating a Perfect Square Trinomial • In the following perfect square trinomial, the constant term is missing. X2 + 14x + ____ • Find the constant term by squaring half the coefficient of the linear term. • (14/2)2 X2 + 14x + 49

  5. Perfect Square Trinomials • Create perfect square trinomials. • x2 + 20x + ___ • x2 - 4x + ___ • x2 + 5x + ___ 100 4 25/4

  6. 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

  7. 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.

  8. 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.

  9. Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side Remember: That when you take the square root to take a positive and negative answer. 2 Answers=2 x intercepts

  10. Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve

  11. Let’s do one more example together-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.

  12. 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.

  13. 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.

  14. Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

  15. Why did this last answer have an imaginary number? What does that mean about the graph of this equation? • It means that the parabola does not cross the x-axis.

  16. Now you are up  Try the following examples. Do your work on your paper and then check your answers.

  17. Homework • Page 237 #29-45 odd, and 11

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