1. Warm Up  Find the roots

2. Solving Quadratic Equations by Completing the Square

3. Objective: Objective: We are gong to create our own Perfect Square Trinomials. In order to solve quadratic equations more effectively. l Examples l x 2 + 6x + 9 l x 2 - 10x + 25 l x 2 + 12x + 36

4. 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

5. Perfect Square Trinomials l Create perfect square trinomials. l x 2 + 20x + ___ l x 2 - 4x + ___ l x 2 + 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