Higher June 2022 Unit 1 Q2
2. The table below shows some of the values of \(y = x^2 + x - 4\) for values of \(x\) from –3 to 3.
| \(x\) | –3 | –2 | –1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| \(y = x^2 + x - 4\) | 2 | –2 | – 4 | 2 | 8 |
(a) Complete the table by finding the values of \(y\) for \(x\) = –1 and for \(x\) = 1. [2]
(b) On the graph paper below, draw the graph of \(y = x^2 + x - 4\) for values of \(x\) from –3 to 3. [2]
(c) Use your graph to solve the equation \(x^2 + x - 4 = 0\) .
Give your answers correct to 1 decimal place. [1]
Give your answers correct to 1 decimal place. [1]
\(x =\) …………………… or \(x =\) ……………………
| Scheme | Marks | Comments |
|---|---|---|
| –4 –2 | B2 | B1 for each |
| Scheme | Marks | Comments |
|---|---|---|
| At least 5 correct plots and no incorrect plot. | P1 | FT ‘their (–1,−4)’ and ‘their (1,−2)’ Allow ± ‘½ a small square’. |
A smooth curve drawn through their plots. | C1 | FT ‘their 7 plots’ OR a curve through the 5 given points AND (−1,–4) and (1,–2). Allow the intention to pass through their plots (within 1 small square, either horizontally or vertically of the point). |
| Scheme | Marks | Comments |
|---|---|---|
| –2·6 AND 1·6 | B1 | Strict FT ‘their curve’ only if exactly two points of intersection with the \(x\)-axis. Answers must be written to one decimal place. Allow ± ‘up to but not including 1 small square’. |