The table below shows the values of the relation \(y = 11 - 2x - 2x^{2}\) for \(-4 \leq x \leq 3\).
x
-4
-3
-2
-1
0
1
2
3
y
-13
11
(a) Copy and complete the table.
(b) Using a scale of 2 cm to 1 unit on the x- axis and 2 cm to 5 units on the y- axis, draw the graph of \(y = 11 - 2x - 2x^{2}\).
(c) Use your graph to find : (i) the roots of the equation \(11 - 2x - 2x^{2} = 0\) ; (ii) the values of x for which \(3 - 2x - 2x^{2} = 0\) ; (iii) the gradient of the curve at x = 1.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
x
-4
-3
-2
-1
0
1
2
3
\(x^{2}\)
16
9
4
1
0
1
4
9
\(11\)
11
11
11
11
11
11
11
11
\(-2x\)
8
6
4
2
0
-2
-4
-6
\(-2x^{2}\)
-32
-18
-8
-2
0
-2
-8
-18
y
-13
-1
7
11
11
7
-1
-13
(b)
(c)(i) x = -2.9 or 1.9
(ii) \(y + (3 - 2x - 2x^{2}) = 11 - 2x - 2x^{2}\)
\(y = 11 - 2x - 2x^{2} - 3 + 2x + 2x^{2}\)
\(y = 8\)
\(\therefore x = \text{-1.8 or 0.8}\)
(iii) \(y = 11 - 2x - 2x^{2}\)
\(\frac{\mathrm d y}{\mathrm d x} = -2 - 4x\)
Gradient at x = 1 : \(-2 - 4(1) = -2 - 4 = -6\)
Source: Myschool Past Questions Archive (Record #53313)