June 2018 Paper 1 Q19
19 Write \(\quad 2x^2 - 16x + 13 \quad\) in the form \(\quad a(x + b)^2 + c \quad\) where \(a\), \(b\) and \(c\) are integers. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| sight of \(2(x^2 - 8x \ldots\ldots)\) | M1 | |
| sight of \(2(x - 4)^2 \ldots\ldots\) | M1dep | |
| \(2[(x - 4)^2 - 16] + 13\) or \(2(x - 4)^2 - 32 + 13\) or \(2[(x - 4)^2 - 16 + 6.5]\) | M1dep | |
| \(2(x - 4)^2 - 19\) | A1 | or \(a = 2\), \(b = -4\), \(c = -19\) |
| Alternative method 2 | ||
| \(a = 2\) | B1 | |
| \(-16 = 2ab\) or \(-16 = 4b\) or \(13 = ab^2 + c\) or \(13 = 2b^2 + c\) | M1 | |
| \(-16 = 2ab\) and \(13 = ab^2 + c\) or \(-16 = 4b\) and \(13 = 2b^2 + c\) | M1dep | oe |
| \(2(x - 4)^2 - 19\) | A1 | or \(a = 2\), \(b = -4\), \(c = -19\) |