(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 \(8x^{2} - 2x - 5 = 0\)
(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) see the diagram above
(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.
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