Completing the Square (Year 10)
Free printable UK Year 10 (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.
✓ Answer key checked by math, never wrong
Grade 9 · 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 + 8x + 20 in the form (x + p)² + q.
- 2.Write x² + 10x + 22 in the form (x + p)² + q.
- 3.Write x² - 6x + 7 in the form (x + p)² + q.
- 4.Solve x² - 10x = 0 by completing the square. Give exact answers.
- 5.Solve x² - 10x + 18 = 0 by completing the square. Give exact answers.
- 6.Solve x² - 4x - 3 = 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 + 2x - 1, 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 - 4x + 7, 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 + 4x - 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 + 10x + 26, and state whether it is a maximum or a minimum.
Made with ChalkBee · chalkbee.com