Higher June 2023 Paper 2 Q26
26 Here is a sketch of \(\quad y = x^2\)
(a) The minimum point of \(\quad y = x^2 \quad\) is at (0, 0)
Write down the coordinates of the minimum point of \(\quad y = x^2 + 2\) [1 mark]
(b) The graph \(\quad y = x^2 \quad\) is reflected in the \(x\) axis.
Write down the equation of the graph after this transformation. [1 mark]
(c) \(y = x^2 \quad\) is now transformed to give \(\quad y = (x + 3)^2\)
Describe fully this single transformation. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| (0, 2) | B1 |
| Answer | Mark | Comments |
|---|---|---|
| \(y = -x^2\) | B1 | oe equation eg \(x^2 = -y\) |
Additional guidance
| \(y = -1x^2 + 0\) | B1 |
| \(y = -(x^2)\) | B1 |
| \(-x^2\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| Translation | B1 | allow eg translate(d) |
| \(\begin{pmatrix} -3 \\ 0 \end{pmatrix}\) | B1 |
Additional guidance
| Do not accept a vector given as coordinates or with missing brackets or with ‘fraction line’ | |
| Translation from (0, 0) | B1B0 |
| Translation horizontally by 3 | B1B0 |
| Translate 3 to the left and 3 down | B1B0 |
| Reflect by \(\begin{pmatrix} -3 \\ 0 \end{pmatrix}\) | B0B1 |
| Giving a combined transformation is B0B0 Rotate by \(\begin{pmatrix} -3 \\ 0 \end{pmatrix}\) and reflect in the \(x\)-axis | B0B0 |
| Ignore references to movement if vector is correct eg Move to the right by \(\begin{pmatrix} -3 \\ 0 \end{pmatrix}\) | B0B1 |