(a) Copy and complete the following table for the relation (y = frac{5}{2} + x – 4x^{2})
| x | -2.0 | -1.5 | -1.0 | -0.5 | 0 | 0.5 | 1 | 1.5 | 2.0 |
| y | -15.5 | 1 | 2.5 |
(b) Using a scale of 2cm to 1 unit on the x- axis and 2cm to 5 units on the y- axis, draw the graph of the relation for (-2.0 leq x leq 2.0).
(c) What is the maximum value of y?
(d) From your graph, obtain the roots of the equation (8x^{2} – 2x – 5 = 0)
Explanation
(a)
| x | -2.0 | -1.5 | -1.0 | -0.5 | 0 | 0.5 | 1 | 1.5 | 2.0 |
| y | -15.5 | -8.0 | -2.5 | 1 | 2.5 | 2.0 | -0.5 | -5.0 | -11.5 |
(b)
(c) The maximum value of y = 2.5.
(d) Obtaining the root of (8x^{2} – 2x – 5 = 0)
Divide both sides by -2, i.e (-4x^{2} + x + frac{5}{2} = 0)
(therefore text{Roots are } x = -0.7 ; x = 0.8.