The table below shows the values of the relation (y = 11 – 2x – 2x^{2}) for (-4 leq x leq 3).
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | -13 | 11 |
(a) Copy and complete the table.
(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 = 11 – 2x – 2x^{2}).
(c) Use your graph to find : (i) the roots of the equation (11 – 2x – 2x^{2} = 0) ; (ii) the values of x for which (3 – 2x – 2x^{2} = 0) ; (iii) the gradient of the curve at x = 1.
Explanation
(a)
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| (x^{2}) | 16 | 9 | 4 | 1 | 0 | 1 | 4 | 9 |
| (11) | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 |
| (-2x) | 8 | 6 | 4 | 2 | 0 | -2 | -4 | -6 |
| (-2x^{2}) | -32 | -18 | -8 | -2 | 0 | -2 | -8 | -18 |
| y | -13 | -1 | 7 | 11 | 11 | 7 | -1 | -13 |
(b)
(c)(i) x = -2.9 or 1.9
(ii) (y + (3 – 2x – 2x^{2}) = 11 – 2x – 2x^{2})
(y = 11 – 2x – 2x^{2} – 3 + 2x + 2x^{2})
(y = 8)
(therefore x = text{-1.8 or 0.8})
(iii) (y = 11 – 2x – 2x^{2})
(frac{mathrm d y}{mathrm d x} = -2 – 4x)
Gradient at x = 1 : (-2 – 4(1) = -2 – 4 = -6)