(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 \(x^{2} – 2x – 4\frac{1}{2} = 0\) ; (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) \(x^{2} - 2x - 4\frac{1}{2} = 0\)
\(x^{2} - 2x - 4\frac{1}{2} + 2\frac{1}{2} = 0 + 2\frac{1}{2}\)
\(x^{2} - 2x - 2 = 2.5\)
When y = 2.5, \(x = \text{-1.3 or 3.3}\).
(iii) Line of symmetry at x = 1.