October 2021 Paper 3 Q1
1
(a) Express \(x^2 + 8x + 2\) in the form \((x + a)^2 + b\). [2]
(b) Write down the coordinates of the turning point of the curve \(y = x^2 + 8x + 2\). [1]
(c) State the transformation(s) which map(s) the curve \(y = x^2\) onto the curve \(y = x^2 + 8x + 2\). [2]
| Scheme | Marks | AO |
|---|---|---|
| \(a = 4\) | B1 | 1.1a |
| \(b = -14\) | B1 | 1.1 |
| [2] |
Notes
May be seen as \((x + 4)^2 - 14\)
| Scheme | Marks | AO |
|---|---|---|
| \((-4, -14)\) | B1 | 2.2a |
| [1] |
Notes
B1: FT their (a)
| Scheme | Marks | AO |
|---|---|---|
| Translation | B1 | 1.2 |
| \(\begin{pmatrix}-4\\-14\end{pmatrix}\) oe | B1 | 2.2a |
| [2] |
Notes
B1: If other transformations as well (eg stretch) then B0
‘Shift’ does not score
B1: FT their (a)
Or B1 for translation 4 to left oe
Or B1 for translation 14 down oe
B0 B1 can be awarded for eg Translation, correct vector & stretch