Converting from general to vertex form by completing the square

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Intros
Lessons
  1. Introduction to completing the square using the "6-step approach": y=2x2−12x+10y=2x^2-12x+10
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Examples
Lessons
  1. Completing the square with NO COEFFICIENT in front of the x2x^2 term
    Convert a quadratic function from general form to vertex form by completing the square.
    y=x2+3x−1y=x^2+3x-1
    1. Completing the square with a NEGATIVE COEFFICIENT in front of the x2x^2 term
      Convert a quadratic function from general form to vertex form by completing the square.
      y=−3x2−60x−50y=-3x^2-60x-50
      1. Completing the square with a RATIONAL COEFFICIENT in front of the x2x^2 term
        Convert a quadratic function from general form to vertex form by completing the square.
        y=12x2+x−52y= \frac{1}{2}x^2+x- \frac{5}{2}
        1. Completing the square with NO CONSTANT TERM
          Convert a quadratic function from general form to vertex form by completing the square.
          y=5x−x2y=5x-x^2
          Topic Notes
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          Step-by- step approach:
          1. isolate X's on one side of the equation
          2. factor out the leading coefficient of X2X^2
          3. "completing the square"
          • X-side: inside the bracket, add (half of the coefficient of X)2X)^2
          • Y-side: add [ leading coefficient (half of the coefficient of X)2X)^2 ]
          4. clean up
          • X-side: convert to perfect-square form
          • Y-side: clean up the algebra
          5. (optional)
          If necessary, determine the vertex now by setting both sides of the equation equal to ZERO.
          6. move the constant term from the Y-side to the X-side, and we have a quadratic function in vertex form!