Intermediate November 2018 Unit 2 Q12
12. The table below shows some of the values of \(y = x^2 + 4x - 1\) for values of \(x\) from –5 to 2.
| \(x\) | –5 | –4 | –3 | –2 | –1 | 0 | 1 | 2 |
|---|---|---|---|---|---|---|---|---|
| \(y = x^2 + 4x - 1\) | 4 | –1 | –4 | –4 | –1 | 4 |
(a) Complete the table by finding the value of \(y\) for \(x = -2\) and for \(x = 2\). [2]
(b) On the graph paper below, draw the graph of \(y = x^2 + 4x - 1\) for values of \(x\) from –5 to 2. [2]
(c) Draw the line \(y = 2\) on the graph paper.
Write down the values of \(x\) where the line \(y = 2\) cuts the curve \(y = x^2 + 4x - 1\). [2]
Write down the values of \(x\) where the line \(y = 2\) cuts the curve \(y = x^2 + 4x - 1\). [2]
Values of \(x\) are ……………………… and ………………………
| Scheme | Marks | Comments |
|---|---|---|
| −5 11 | B2 | B1 for each. Table takes precedence if conflicting values given. |
| Scheme | Marks | Comments |
|---|---|---|
| At least 6 correct plots and no incorrect plot. | P1 | F.T. ‘their (−2,−5)’ and ‘their (2,11)’ OR (−2,−5) and (2,11) plotted. Allow ± ‘½ a small square’. Ignore any plots that can not be shown e.g. (−2,−13). |
| A smooth curve drawn through their plots. | C1 | F.T. ‘their plots’. OR a curve through the 6 given points and (−2,–5) and (2,11). Allow intention to pass through their plots. (± 1 small square horizontal or vertical.) |
| Scheme | Marks | Comments |
|---|---|---|
| Line y = 2 drawn | L1 | Must be at least 2cm long. |
| −4·65 AND 0·65 | B1 | F.T. intersection of ‘their curve’ with ‘their y = 2’ only if exactly two points of intersection. Allow ± ‘1 small square’. |