# Converting from general to vertex form by completing the square

##### Intros

###### Lessons

##### Examples

###### Lessons

**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.

$y=x^2+3x-1$**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.

$y=-3x^2-60x-50$**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.

$y= \frac{1}{2}x^2+x- \frac{5}{2}$**Completing the square with NO CONSTANT TERM**

Convert a quadratic function from general form to vertex form by completing the square.

$y=5x-x^2$

###### Free to Join!

StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.

#### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.#### Make Use of Our Learning Aids

#### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.#### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Notes

Step-by- step approach:

1. isolate X's on one side of the equation

2. factor out the

3. "completing the square"

• X-side: inside the bracket, add (half of the coefficient of $X)^2$

• Y-side: add [

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. 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!

###### Basic Concepts

2

videos

remaining today

remaining today

5

practice questions

remaining today

remaining today