The following is an incomplete table for the relation (y = 2x^{2} – 5x + 1)
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
| y | 8 | 1 | -1 | 26 |
(a) Copy and complete the table.
(b) Using a scale of 2cm to 1 unit on the x- axis and 2cm to 10 units on the y- axis, draw the graph of the relation (y = 2x^{2} – 5x + 1) for (-3 leq x leq 5).
(c) Using the same scale and axes, draw the graph of (y = x + 6).
(d) Estimate from your graphs, correct to one decimal place : (i) the least value of y and the value of x for which it occurs ; (ii) the solution of the equation (2x^{2} – 5x + 1 = x + 6).
Explanation
(a) (y = 2x^{2} – 5x + 1)
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
| y | 34 | 19 | 8 | 1 | -2 | -1 | 4 | 13 | 26 |
Table of value for (y = x + 6)
| x | -2 | 0 | 2 |
| y | 4 | 6 | 8 |
(b)
(d) (i) Least value of y = -2 occurs at x = 1
(ii) Solution of (2x^{2} – 5x + 1 = x + 6) are x = -0.7 and x = 3.7.