(a) Copy and complete the table.
(y = x^{2} – 2x – 2) for (-4 leq x leq 4)
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| y | 22 | -2 | 1 | 6 |
(b) Using a scale of 2 cm to 1 unit on the x- axis and 2 cm to 5 units on the y- axis, draw the graph of (y = x^{2} – 2x – 2).
(c) Use your graph to find : (i) the roots of the equation (x^{2} – 2x – 2 = 0) ; (ii) the values of x for which (x^{2} – 2x – 4frac{1}{2} = 0) ; (iii) the equation of the line of symmetry of the curve.
Explanation
(a) (y = x^{2} – 2x – 2)
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| (x^{2}) | 16 | 9 | 4 | 1 | 0 | 1 | 4 | 9 | 16 |
| (-2x) | 8 | 6 | 4 | 2 | 0 | -2 | -4 | -6 | -8 |
| (-2) | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 |
| (y) | 22 | 13 | 6 | 1 | -2 | -3 | -2 | 1 | 6 |
(b)
(c)(i) (x^{2} – 2x – 2 = 0)
(therefore y = 0 ; x = text{-0.7 or 2.7})
(ii) (x^{2} – 2x – 4frac{1}{2} = 0)
(x^{2} – 2x – 4frac{1}{2} + 2frac{1}{2} = 0 + 2frac{1}{2})
(x^{2} – 2x – 2 = 2.5)
When y = 2.5, (x = text{-1.3 or 3.3}).
(iii) Line of symmetry at x = 1.