Home > Grade Levels > High School Algebra >

Completing the Square in a Quadratic Expression

Answer Keys Here

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: ax2 + 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 - (b2/4a) Let's learn how to complete a square. Suppose that you have an equation like this x2 + 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: x2 + bx can be converted to nearly a square. In algebraic form it will look something like this: x2 + 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

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.

  • Quiz 1 - Lots of holes in here, like Swiss cheese.
  • Quiz 2 - You will need to find variables too.
  • Quiz 3 - That y variable is a mess.