(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) see graph above
(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