# 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 $X^2$
3. “completing the square”
• X-side: inside the bracket, add (half of the coefficient of $X)^2$
• Y-side: add [ leading coefficient (half of the coefficient of $X)^2$ ]
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”: $y=2x^2-12x+10$

• 2.
Completing the square with NO COEFFICIENT in front of the $x^2$ term
Convert a quadratic function from general form to vertex form by completing the square.
$y=x^2+3x-1$

• 3.
Completing the square with a NEGATIVE COEFFICIENT in front of the $x^2$ term
Convert a quadratic function from general form to vertex form by completing the square.
$y=-3x^2-60x-50$

• 4.
Completing the square with a RATIONAL COEFFICIENT in front of the $x^2$ term
Convert a quadratic function from general form to vertex form by completing the square.
$y= \frac{1}{2}x^2+x- \frac{5}{2}$

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