Allday Education

Free Completing the Square Worksheet

Ten completing-the-square problems with a worked answer key.

Answer key included
Name: Date:
Completing the Square
1.
x2+2x−2x^2 + 2x - 2
2.
x2−2x−7x^2 - 2x - 7
3.
x2−4x−3x^2 - 4x - 3
4.
x2+6x−9x^2 + 6x - 9
5.
x2+6x−2x^2 + 6x - 2
6.
x2+10x+2x^2 + 10x + 2
7.
x2+10x+1x^2 + 10x + 1
8.
x2−12x−5x^2 - 12x - 5
9.
x2+2x−6x^2 + 2x - 6
10.
x2−12x+6x^2 - 12x + 6
Andy · alldayeverydaymath.com
Name: Answer KeyDate:
Completing the Square
1.
x2+2x−2x^2 + 2x - 2
Answer: (x+1)2−3(x + 1)^2 - 3
2.
x2−2x−7x^2 - 2x - 7
Answer: (x−1)2−8(x - 1)^2 - 8
3.
x2−4x−3x^2 - 4x - 3
Answer: (x−2)2−7(x - 2)^2 - 7
4.
x2+6x−9x^2 + 6x - 9
Answer: (x+3)2−18(x + 3)^2 - 18
5.
x2+6x−2x^2 + 6x - 2
Answer: (x+3)2−11(x + 3)^2 - 11
6.
x2+10x+2x^2 + 10x + 2
Answer: (x+5)2−23(x + 5)^2 - 23
7.
x2+10x+1x^2 + 10x + 1
Answer: (x+5)2−24(x + 5)^2 - 24
8.
x2−12x−5x^2 - 12x - 5
Answer: (x−6)2−41(x - 6)^2 - 41
9.
x2+2x−6x^2 + 2x - 6
Answer: (x+1)2−7(x + 1)^2 - 7
10.
x2−12x+6x^2 - 12x + 6
Answer: (x−6)2−30(x - 6)^2 - 30
Andy · alldayeverydaymath.com

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About this worksheet

Students complete the square to rewrite a quadratic — the move behind the quadratic formula and vertex form. Numbers keep the perfect-square step clean so the method stays visible.

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