(a) Copy and complete the following table of values for (y = 2x^{2} – 9x – 1).
| x | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| y | -1 | -8 | -11 | 17 |
(b) Using a scale of 2cm to represent 1 unit on the x- axis and 2cm to represent 5 units on the y- axis, draw the graph of (y = 2x^{2} – 9x – 1).
(c) Use your graph to find the : (i) roots of the equation (2x^{2} – 9x = 4), correct to one decimal place ; (ii) gradient of the curve (y = 2x^{2} – 9x – 1) at x = 3.
Explanation
(a)
| x | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| y | 10 | -1 | -8 | -11 | -10 | -5 | 4 | 17 |
(b)
(c)(i) (2x^{2} – 9x = 4)
(2x^{2} – 9x – 1 = 4 – 1 = 3)
At y = 3, x = 0.2 and 4.3.
(ii) Gradient of (y = 2x^{2} – 9x – 1) at x = 3
= (frac{BC}{AB} = frac{9.5}{4.3})
= (2.2)