# Find The Missing Term To Complete The Square Worksheet

Assignment will be available soon

Completing the square is a technique used to transform a quadratic expression into a perfect square trinomial. To find the missing term needed to complete the square, we modify the quadratic expression like $$ax^2 + bx$$ by adding \left(\frac{b}{2a}\right)^2. By adding this term, we can rewrite the expression as a perfect square trinomial. In these worksheets, students will identify and add the missing term \left(\frac{b}{2a}\right)^2.

Example: Complete the square for the expression k^2 - 20k + "_____".

Algebra 2

## How Will This Worksheet on “Find the Missing Term to Complete the Square” Benefit Your Student's Learning?

• It improves problem-solving skills by offering students a valuable alternative to the quadratic formula
• It also deepens their understanding of the structure of quadratic functions.
• Promotes critical thinking, as students must use logical reasoning and a step-by-step approach.
• Establishes a solid foundation for advanced mathematical topics such as integration and solving differential equations.

## How to Find the Missing Term to Complete the Square?

• Determine the values of $$a$$, $$b$$, and $$c$$ in the given quadratic expression.
• Add \left(\frac{b}{2a}\right)^2 to the expression.
• Simplify the expression to find the missing term.

## Solved Example

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.$\newline$$z^2 - 18z + \underline{\hspace{2em}}$
Solution:
1. Identify Coefficients: Identify the coefficients of the polynomial $z^2 - 18z + \_$ to compare with the standard quadratic form $ax^2 + bx + c$.
$a = 1$ (coefficient of $z^2$)
$b = -18$ (coefficient of $z$)
$c = ?$ (the number we need to find)
2. Calculate Completing Square Value: To complete the square, we need to add $(\frac{b}{2})^2$ to the polynomial. In this case, $b$ is $-18$.$\newline$Calculate $(-\frac{18}{2})^2$ to find the value that completes the square.$\newline$$(-\frac{18}{2})^2 = (-9)^2 = 81$
3. Add to Complete Square: The number that completes the square is $81$. So the polynomial becomes a perfect-square quadratic when we add $81$. The completed square form is $z^2 - 18z + 81$.

### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”