Converting from general to vertex form by completing the square

Converting from general to vertex form by completing the square

Lessons

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!
  • 1.
    Introduction to completing the square using the “6-step approach”: y=2x212x+10y=2x^2-12x+10

  • 2.
    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+3x1y=x^2+3x-1

  • 3.
    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=3x260x50y=-3x^2-60x-50

  • 4.
    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+x52y= \frac{1}{2}x^2+x- \frac{5}{2}

  • 5.
    Completing the square with NO CONSTANT TERM
    Convert a quadratic function from general form to vertex form by completing the square.
    y=5xx2y=5x-x^2