(a) Copy and complete the following table of values for the relation (y = x^{2} – 2x – 5)
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
| y | -2 | -6 | -2 | 3 | 10 |
(b) Draw the graph of the relation (y = x^{2} – 2x – 5); using a scale of 2 cm to 1 unit on the x- axis, and 2 cm to 2 units on the y- axis.
(c) Using the same axes, draw the graph of (y = 2x + 3).
(d) Obtain in the form (ax^{2} + bx + c = 0) where a, b and c are integers, the equation which is satisfied by the x- coordinate of the points of intersection of the two graphs.
(e) From your graphs, determine the roots of the equation obtained in (d) above.
Explanation
(a)
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
| (x^{2}) | 9 | 4 | 1 | 0 | 1 | 4 | 9 | 16 | 25 |
| (-2x) | 6 | 4 | 2 | 0 | -2 | -4 | -6 | -8 | -10 |
| -5 | -5 | -5 | -5 | -5 | -5 | -5 | -5 | -5 | -5 |
| y | 10 | 3 | -2 | -5 | -6 | -5 | -2 | 3 | 10 |
(b)
(c)
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
| (2x) | -6 | -4 | -2 | 0 | 2 | 4 | 6 | 8 | 10 |
| -3 | -3 | -3 | -3 | -3 | -3 | -3 | -3 | -3 | -3 |
| y | -9 | -7 | -5 | -3 | -1 | 1 | 3 | 5 | 7 |
(d) (x^{2} – 2x – 5 = 2x – 3)
(x^{2} – 2x – 2x – 5 + 3 = 0)
(x^{2} – 4x – 2 = 0)
(e) x = -0.8 or 4.3