(a) Copy and complete the table of values for the relation \(y = -x^{2} + x + 2; -3 \leq x \leq 3\).
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | -4 | 2 | -4 |
(b) Using scales of 2 cm to 1 unit on the x- axis and 2 cm to 2 units on the y- axis, draw a graph of the relation \(y = -x^{2} + x + 2\).
(c) From the graph, find the : (i) minimum value of y ; (ii) roots of equation \(x^{2} – x – 2 = 0\) ; (iii) gradient of the curve at x = -0.5.
Explanation
(a)
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | -10 | -4 | 0 | 2 | 2 | 0 | -4 |
(b) 
(c) (ii) roots of the equation : \(x^{2} - x - 2 = 0\) are x = -1 or x = 2.
(iii) gradient of the curve at x = -0.5 is 2.1.