Questions: Completing the square
Before attempting these questions, it is highly recommended that you read Guide: Completing the square.
Q1
Express each of the following quadratic expressions in the form \((x+p)^2 + q\), where \(p,q\) are numbers.
1.1. \(\quad x^2 - 2x + 15\).
1.2. \(\quad y^2 - 6y + 8\).
1.3. \(\quad x^2 + 8x + 20\).
1.4. \(\quad m^2 - 26m + 25\)
1.5. \(\quad n^2 + 6n + 50\).
1.6. \(\quad x^2 + 2x + 144\).
1.7. \(\quad h^2 - 3h - 3\).
1.8. \(\quad x^2 + x - 3\).
1.9. \(\quad x^2 - 13x + 43\).
1.10. \(\quad y^2 - 8y + 16\).
1.11. \(\quad x^2 + 13x + 9\).
1.12. \(\quad m^2 + 3m + 33\).
Q2
Express each of the following quadratic expressions in the form \(a(x+p)^2 + q\), where \(a,p,q\) are numbers.
2.1. \(\quad 2x^2 - 12x + 14\).
2.2. \(\quad 5y^2 - 10y + 4\).
2.3. \(\quad 4x^2 + 32x + 68\).
2.4. \(\quad 2m^2 + 2m + 2\)
2.5. \(\quad 3x^2 - 2x + 5\).
2.6. \(\quad 4x^2 - 4x + 1\).
2.7. \(\quad 2h^2 - 3h + 1\).
2.8. \(\quad 3x^2 + 5x + 2\).
Q3
Using your working from Q1 and Q2, solve the following quadratic equations.
3.1. \(\quad y^2 - 6y + 8 = 0\).
3.2. \(\quad m^2 - 26m + 25 = 0\).
3.3. \(\quad x^2 + 8x + 20 = 0\).
3.4. \(\quad 4x^2 - 4x + 1 = 0\).
3.5. \(\quad 4x^2 + 32x + 68 = 0\).
3.6. \(\quad 3x^2 + 5x + 2 = 0\).
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 09/24 by tdhc.