Complete the Square Worksheets Grade 9

Algebra

Quadratic Expressions

Each printable worksheet below is a full page of practice problems and comes with an answer key that explains how to solve every problem, step by step. Open a worksheet and use the Print / Save as PDF button to download it.

Worksheet 1

9 problems
  1. x² + 12x + 32 = (x + ?)² + ?
  2. x² + 6x + 5 = 0
  3. x² + 8x + 10 = (x + ?)² + ?

…and 6 more problems

Open & Print Worksheet 1

Worksheet 2

8 problems
  1. x² + 14x + 41 = (x + ?)² + ?
  2. x² - 6x + 5 = (x - ?)² - 4
  3. A rectangular garden has a length that is 4 meters more than its width. If the area of the garden is 96 square meters, what is the width of the garden in meters?

…and 5 more problems

Open & Print Worksheet 2

Worksheet 3

8 problems
  1. Noah is designing a rectangular fountain for a city plaza. The length of the fountain is 6 meters more than its width. The area of the fountain is 91 square meters. By rewriting the area equation in the form (x + h)² + k, find the width of the fountain in meters.
  2. A rectangular garden has a length that is 4 meters longer than its width. If the area of the garden is 96 square meters, find the dimensions of the garden by completing the square to solve for the width.
  3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (8,0), and (0,6). A circle is circumscribed around the triangle such that all three vertices lie on the circle's circumference. What is the area of the circle? (Use π = 3.14)

…and 5 more problems

Open & Print Worksheet 3

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