(a) Copy and complete the table.
\(y = x^{2} - 2x - 2\) for \(-4 \leq x \leq 4\)
x
-4
-3
-2
-1
0
1
2
3
4
y
22
-2
1
6
(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 \(y = x^{2} - 2x - 2\).
(c) Use your graph to find : (i) the roots of the equation \(x^{2} - 2x - 2 = 0\) ; (ii) the values of x for which \(x^{2} - 2x - 4\frac{1}{2} = 0\) ; (iii) the equation of the line of symmetry of the curve.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a) \(y = x^{2} - 2x - 2\)
x
-4
-3
-2
-1
0
1
2
3
4
\(x^{2}\)
16
9
4
1
0
1
4
9
16
\(-2x\)
8
6
4
2
0
-2
-4
-6
-8
\(-2\)
-2
-2
-2
-2
-2
-2
-2
-2
-2
\(y\)
22
13
6
1
-2
-3
-2
1
6
(b)
(c)(i) \(x^{2} - 2x - 2 = 0\)
\(\therefore y = 0 ; x = \text{-0.7 or 2.7}\)
(ii) \(x^{2} - 2x - 4\frac{1}{2} = 0\)
\(x^{2} - 2x - 4\frac{1}{2} + 2\frac{1}{2} = 0 + 2\frac{1}{2}\)
\(x^{2} - 2x - 2 = 2.5\)
When y = 2.5, \(x = \text{-1.3 or 3.3}\).
(iii) Line of symmetry at x = 1.
Source: Myschool Past Questions Archive (Record #53120)