Higher January 2022 Paper 1 Q20
20
(a) Express \(7 + 12x - 3x^2\) in the form \(a + b(x + c)^2\) where \(a\), \(b\) and \(c\) are integers. (3)
C is the curve with equation \(y = 7 + 12x - 3x^2\)
The point \(A\) is the maximum point on C
(b) Use your answer to part (a) to write down the coordinates of \(A\) (1)
| Scheme | Marks |
|---|---|
| \(7 - 3(x^2 - 4x)\) | M1 |
| \(7 - 3[(x - 2)^2 - 4]\) | M1 |
| \(19 - 3(x - 2)^2\) | A1 |
| (3) |
Notes
M1: or for one of \(a\), \(b\) or \(c\) correct
M1: or for two of \(a\), \(b\) or \(c\) correct
| Scheme | Marks |
|---|---|
| (2, 19) | B1 |
| (1) | |
| (4 marks) |
Notes
B1: ft their expression