## Completing the Square in a Quadratic Expression

#### Aligned To Common Core Standard:

**High School** - HSA-SSE.B.3b

How to Complete the Square in a Quadratic Expression - What is a quadratic equation? A quadratic equation is where we convert an equation that looks like this: ax^{2} + bx + c = 0 into something like this: a(x+d)^{2} + e = 0.
For those who don't know, D = b/2a and e = c - (b^{2}/4a)
Let's learn how to complete a square.
Suppose that you have an equation like this x^{2} + bx if you have X twice in the equation that can make solving the equation a bit tricky. So, what can be done?
Taking some inspirations from the rules of geometry, we can convert it like this:
x^{2} + bx can be converted to nearly a square. In algebraic form it will look something like this:
x^{2} + bx + (b/2)^{2} = (x+b/2)^{2}
Hence, completing the square
So, when you add (b/2)^{2} , the square can be completed and (x + b/2)^{2} has x only once which is far easier to use. These worksheets and lessons have students add a term to convert a quadratic expression into a square of a binomial.

### Printable Worksheets And Lessons

- Missing Parts Step-by-step
Lesson- You need to create a square quadratic by adding terms
that are currently blank.

- Guided Lesson
- Once again, solve each problem by supplying the lost term.

- Guided Lesson Explanation
- Everything on here will give you any idea of the level of patience
that you will need to complete these regularly.

- Practice Worksheet
- A let drill and kill always helps us get better.

- Matching Worksheet
- Match the partial quadratics to their missing pieces.

- Completing the Square Five
Worksheet Pack - A very large practice pack for you to work
away at.

#### Homework Sheets

It is definitely best to start off slow with this one.

- Homework 1 - Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.
- Homework 2 - We are missing the whole number portion of the quadratic.
- Homework 3 - Find the missing value to create a perfect-square.

#### Practice Worksheets

I provided a lot of space for students to put their work on these.

- Practice 1 - What is missing?
- Practice 2 - Lots of new variables for you to play with.
- Practice 3 - What whole number is missing from each expression?

#### Math Skill Quizzes

After the first quiz, they should have this skill down pat.