(a) Copy and complete the table of values for the relation \(y = 5 - 7x - 6x^{2}\) for \(-3 \leq x \leq 2\).
x
-3
-2
-1
-0.5
0
1
2
y
-28
6
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 : (i) graph of \(y = 5 - 7x - 6x^{2}\) ; (ii) line \(y = 3\) on the same axis. (c) Use your graph to find the : (i) roots of the equation \(2 - 7x - 6x^{2} = 0\) ; (ii) maximum value of \(y = 5 - 7x - 6x^{2}\).
Explanation
x
-3
-2
-1
-0.5
0
1
2
y
-28
-5
6
7
5
-8
-33
(b)(i) (c)(i) \(2 - 7x - 6x^{2} = 0\) \(2 + 3 - 7x - 6x^{2} = 3\) \(5 - 7x - 6x^{2} = 3\) \(\therefore \text{the roots at y = 3 are } x = -1.4; 0.2\) (ii) Maximum value of \(y = 5 - 7x - 6x^{2}\) is y = 7.
