(a) Draw the table of values for the relation (y = x^{2}) for the interval (-3 leq x leq 4).
(b) Using a scale of 2 cm to 1 unit on the x- axis and 2 cm to 2 units on the y- axis, draw the graphs of : (i) (y = x^{2}) ; (ii) (y = 2x + 3) for (-3 leq x leq 4).
(c) Use your graph to find : (i) the roots of the equation (x^{2} = 2x + 3) ; (ii) the gradient of (y = x^{2}) at x = -2.
Explanation
(a)
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| (y = x^{2}) | 9 | 4 | 1 | 0 | 1 | 4 | 9 | 16 |
(b) (y = 2x + 3)
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| 2x | -6 | -4 | -2 | 0 | 2 | 4 | 6 | 8 |
| 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| y | -3 | -1 | 1 | 3 | 5 | 7 | 9 | 11 |
(c)(i) The roots of the equation are -1 and 3, from the graph.
(ii) The gradient of (y = x^{2}) at x = -2 : (frac{8}{-2.5} = -3.2)