Higher January 2019 Paper 2R Q20
20
(a) Write \(3x^2 - 12x + 7\) in the form \(a(x + b)^2 + c\) (3)
The line L is the line of symmetry of the curve with equation \(y = 3x^2 - 12x + 7\)
(b) Using your answer to part (a) or otherwise, write down an equation of L. (1)
| Scheme | Marks |
|---|---|
| \(3(x^2 - 4x) + 7\) or \(3\left(x^2 - 4x + \dfrac{7}{3}\right)\) | M1 |
\(3((x - 2)^2 - 4) + 7\) or \(3\left((x - 2)^2 - 4 + \dfrac{7}{3}\right)\) or \(3(x - 2)^2 - 12 + 7\) | M1 |
| \(3(x - 2)^2 - 5\) | A1 |
| (3) |
Notes
M1: or expanding \(a(x^2 + 2bx + b^2) + c\)
M1: \(-12 = 2ab\) or \(7 = ab^2 + c\)
A1: or \(a = 3\), \(b = -2\), \(c = -5\)
| Scheme | Marks |
|---|---|
| \(x = 2\) | B1 |
| (1) | |
| (4 marks) |
Notes
B1: ft from (a)