# Completing the Square Worksheets

What is "Completing the Square" in Math? It is the method by which you can rewrite the quadratic equation. E.g., ax2 + bx + c into a(x - h)2+k. To graph the parabola, due to a(x - h)2+k, you will know the vertex is at (h, k). Also, if you are finding calculus, then learning how to complete the square may assist you mix a tricky function. If you are getting a session in differential equations, it may assist you to find the change of a function). Steps to Complete the Square - Suppose ax2 + bx + c and complete the square. Value a {the coefficient of x(power2)} out of the first two values only. E.g., a(x2 + b/a x) + c. Divide the coefficient of x by 2, take square then, you will do addition & subtraction inside the brackets (nothing will change whether you add first or subtract vice versa). E.g., a{x2+b/a x+(b/2a)2 – (b/a)2} + c. Bring the new value you are subtracting out from the brackets, but you will multiply it by a. E.g., a{x2 + b/a x + (b/2a)2} +c – a{(b/2a)}2. The value in the brackets are a perfect square! E.g., a( x + b/2a)2 +c – a(b/2a)2.

• ### Basic Lesson

Guides students solving equations that involve an Completing the Squares. Demonstrates answer checking. What value would be placed in the box to create perfect square trinomials? To find the needed value for the perfect square trinomial, take half of the coefficient of the middle term (x-term), square it, and put it in the box.

• ### Intermediate Lesson

Demonstrates how to solve more difficult problems. Keep all x related terms on one side. Move the constant to the right. Be sure that the coefficient of the highest power is one. If it is not, divide each term by that value to create a leading coefficient of one.

• ### Independent Practice 1

A really great activity for allowing students to understand the concept of Completing the Squares.

• ### Independent Practice 2

Students find the Completing the Squares in assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with problems to achieve the concepts of Completing the Squares.

• ### Skill Quiz

This tests the students ability to evaluate Completing the Squares.