Find The Missing Term To Complete The Square Worksheet

Algebra 2
Quadratic Functions

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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.\newlinez218z+z^2 - 18z + \underline{\hspace{2em}}
Solution:
  1. Identify Coefficients: Identify the coefficients of the polynomial z218z+_z^2 - 18z + \_ to compare with the standard quadratic form ax2+bx+cax^2 + bx + c.
    a=1a = 1 (coefficient of z2z^2)
    b=18b = -18 (coefficient of zz)
    c=?c = ? (the number we need to find)
  2. Calculate Completing Square Value: To complete the square, we need to add (b2)2(\frac{b}{2})^2 to the polynomial. In this case, bb is 18-18.\newlineCalculate (182)2(-\frac{18}{2})^2 to find the value that completes the square.\newline(182)2=(9)2=81(-\frac{18}{2})^2 = (-9)^2 = 81
  3. Add to Complete Square: The number that completes the square is 8181. So the polynomial becomes a perfect-square quadratic when we add 8181. The completed square form is z218z+81z^2 - 18z + 81.
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About Worksheet

Algebra 2
Quadratic Functions

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 +` `"_____"`.

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