(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.
