Higher January 2020 Paper 2R Q23
23 Express \(\;7 - 12x - 2x^2\;\) in the form \(\;a + b(x + c)^2\;\) where \(a\), \(b\) and \(c\) are integers.
(3)
| Scheme | Marks |
|---|---|
| \(-2(x^2 + 6x - 3.5)\) or \(-2(x^2 + 6x) + 7\) | M1 |
| \(-2[(x + 3)^2 - 9 - 3.5]\) or \(-2[(x + 3)^2 - 9] + 7\) | M1 |
| \(25 - 2(x + 3)^2\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: Factorising by −2
M1: Completing the square
Alternative method
| Scheme | Marks |
|---|---|
| \(a + b(x^2 + 2cx + c^2)\) \(2bc = -12\) or \(a + bc^2 = 7\) or \(b = -2\) | M1 |
| \(2 \times -2 \times c = -12\) or \(c = 3\) | M1 |
| \(a + -2 \times (3)^2 = 7\) or \(a = 25\) seen | A1 |
Notes
M1: Equating coefficients or stating value of \(b\)
M1: Equating coefficients or stating value of \(c\)
A1: Equating coefficients or stating value of \(a\)
Special Cases:
SC B2 for answer of \(-2(x + 3)^2\) + constant or \(25 - 2(x + \text{positive constant})^2\)
SC B1 for answer of \(-2(x - 3)^2\) + constant