(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 \(y = 5 - 7x - 6x^{2}\).
Verified Correct Answer: .
Step-by-Step Mathematical Solution
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.
Source: Myschool Past Questions Archive (Record #54448)