Completing the Square (Year 11)
Free printable UK Year 11 (GCSE Higher tier) maths worksheet: write quadratics in (x + p)² + q form, solve exactly, and find the turning point of the curve by completing the square.
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Grade 10 · Math worksheet
Name
Date
Math
Completing the Square
Rewrite each quadratic in completed-square form (x + p)² + q, then use that form: to solve the equation exactly (answers may be surds), or to read off the turning point of the curve. Higher tier.
- 1.Write x² + 4x - 1 in the form (x + p)² + q.
- 2.Write x² - 12x + 45 in the form (x + p)² + q.
- 3.Write x² - 8x + 9 in the form (x + p)² + q.
- 4.Solve x² + 4x - 12 = 0 by completing the square. Give exact answers.
- 5.Solve x² - 4x + 2 = 0 by completing the square. Give exact answers.
- 6.Solve x² - 6x + 2 = 0 by completing the square. Give exact answers.
- 7.By completing the square, find the coordinates of the turning point of the curve y = x² - 8x + 21, and state whether it is a maximum or a minimum.
- 8.By completing the square, find the coordinates of the turning point of the curve y = x² - 10x + 20, and state whether it is a maximum or a minimum.
- 9.By completing the square, find the coordinates of the turning point of the curve y = x² + 2x - 5, and state whether it is a maximum or a minimum.
- 10.By completing the square, find the coordinates of the turning point of the curve y = x² - 6x + 13, and state whether it is a maximum or a minimum.
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