Higher November 2023 Paper 5 Q21
21 The graph of \(y = x^2\) is shown below for \(-2 \leqslant x \leqslant 2\).
(a) Find the equation of the image when \(y = x^2\) is reflected in the line \(y = 2\). [2]
(b) Describe the single transformation that maps the graph of \(y = x^2\) onto the graph of \(y = x^2 + 6x - 5\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(y = 4 - x^2\) | 2 | B1 for answer \(y = k - x^2\) | \(k\) is any value including zero |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Translation \(\begin{pmatrix} -3 \\ -14 \end{pmatrix}\) | 4 | B3 for translation \(\begin{pmatrix} -3 \\ k \end{pmatrix}\) or translation \(\begin{pmatrix} k \\ -14 \end{pmatrix}\) OR M2 for [\(y =\)] \((x + 3)^2 - 5 - 3^2\) or better or M1 for [\(y =\)] \((x + 3)^2\) seen B1 for translation | If more than one transformation given then M2 maximum |