Higher June 2023 Paper 1 Q21
21 Express \(\quad x^2 - 6x - 15 \quad\) in the form \(\quad (x - a)^2 - b \quad\) where \(a\) and \(b\) are integers. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((x - 3)^2 - 24\) or \(a = 3\) and \(b = 24\) | B2 | B1 \((x - 3)^2 \ldots\) or \((x - 3)(x - 3) \ldots\) or \(a = 3\) (implied by 3, \(-24\)) or \(x^2 - 2ax + a^2 - b\) or \(-2a = -6\) or \(2a = 6\) or \(a^2 - b = -15\) or correct \(b\) for their \(a\) |
Additional guidance
| \((x + 3)^2 - 24\) (24 is correct for \(a = -3\)) | B1 |
| \((x - 6)^2 - 51\) (51 is correct for \(a = 6\)) | B1 |
| \((x + 6)^2 - 51\) (51 is correct for \(a = -6\)) | B1 |