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Completing the Square with Parabolas. Perfect Square Trinomials. Examples x 2 + 6x + 9 x 2 - 10x + 25 x 2 + 12x + 36. Creating a Perfect Square Trinomial.

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Completing the Square with Parabolas


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    Presentation Transcript
    1. Completing the Square with Parabolas

    2. Perfect Square Trinomials • Examples • x2 + 6x + 9 • x2 - 10x + 25 • x2 + 12x + 36

    3. 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

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

    5. Completing the Square with Parabolas Example 1: Put the following parabola in vertex form by completing the square: Step 1: Move the constant, c, to the other side.

    6. Completing the Square with Parabolas Step 2: Find

    7. Completing the Square with Parabolas Step 3: Take

    8. Completing the Square with Parabolas Step 4: Add to both sides of the equation.

    9. Completing the Square with Parabolas Step 5:Factor the perfect square trinomial.

    10. Completing the Square with Parabolas Step 6: Move the constant back to the right side. Can you identify the vertex of this parabola?

    11. Completing the Square with Parabolas Example 2: Put the following parabola in vertex form by completing the square: Step 1: Move the constant, c, to the other side.

    12. Completing the Square with Parabolas Step 2: Find

    13. Completing the Square with Parabolas Step 3: Take

    14. Completing the Square with Parabolas Step 4: Add to both sides of the equation.

    15. Completing the Square with Parabolas Step 5:Factor the perfect square trinomial.

    16. Completing the Square with Parabolas Step 6: Move the constant back to the right side. Can you identify the vertex of this parabola?

    17. Completing the Square with Parabolas Example 3: Put the following parabola in vertex form by completing the square: Step 1: Move the constant, c, to the other side.

    18. Completing the Square with Parabolas Step 2: Find

    19. Completing the Square with Parabolas Step 3: Take

    20. Completing the Square with Parabolas Step 4: Add to both sides of the equation.

    21. Completing the Square with Parabolas Step 5:Factor the perfect square trinomial.

    22. Completing the Square with Parabolas Step 6: Move the constant back to the right side. Can you identify the vertex of this parabola?

    23. Completing the Square with Parabolas Example 4: Put the following parabola in vertex form by completing the square: Step 1: Move the constant, c, to the other side.

    24. Completing the Square with Parabolas Step 2: Find **In order to complete the square, . **Before we can find , we must factor out the .

    25. Completing the Square with Parabolas Step 3: Take

    26. Completing the Square with Parabolas Step 4: Add to both sides of the equation.

    27. Completing the Square with Parabolas Step 5:Factor the perfect square trinomial.

    28. Completing the Square with Parabolas Step 6: Move the constant back to the right side. Can you identify the vertex of this parabola?

    29. Completing the Square with Parabolas You Try! Put the following parabola in vertex form by completing the square: Can you identify the vertex of this parabola?