Higher June 2025 Unit 1 Q2
2. The table below shows some of the values of \(y = 2x^2 - 6\) for values of \(x\) from –3 to 2.
| \(x\) | –3 | –2 | –1 | 0 | 1 | 2 |
|---|---|---|---|---|---|---|
| \(y = 2x^2 - 6\) | 2 | –4 | –6 | 2 |
(a) Complete the table above. [2]
(b) On the graph paper below, draw the graph of \(y = 2x^2 - 6\) for values of \(x\) from –3 to 2. [2]
(c) Draw the line \(y = 1\) on the graph paper.
Write down the values of \(x\) where the line \(y = 1\) cuts the curve \(y = 2x^2 - 6\).
Give your answers correct to 1 decimal place. [2]
Write down the values of \(x\) where the line \(y = 1\) cuts the curve \(y = 2x^2 - 6\).
Give your answers correct to 1 decimal place. [2]
| Scheme | Marks | Comments |
|---|---|---|
| 12 –4 | B2 | Answers in table take precedence. B1 for each. |
| Scheme | Marks | Comments |
|---|---|---|
| At least 4 correct plots and no incorrect plot. | P1 | FT ‘their (–3,12)’ and ‘their (1,−4)’ OR (–3,12) and (1,−4) plotted (even when not shown in the table or contradicted). Allow ± ‘½ a small square’. Ignore any additional points plotted on the curve. |
A smooth curve drawn through their 6 plots. | C1 | FT for one of the following:
|
| Scheme | Marks | Comments |
|---|---|---|
| –1·9 AND 1·9 | B2 | Answer line takes precedence. Strict FT intersection of ‘their curve’ with \(y = 1\) only if exactly two points of intersection. May be seen in any order. Need not be to one decimal place. Allow ± ‘1 small square’ i.e. ± 0.1. Award B1 for one of the following:
|