(a) Copy and complete the following table of values for the relation \(y = x^{2} - 2x - 5\)
x
-3
-2
-1
0
1
2
3
4
5
y
-2
-6
-2
3
10
(b) Draw the graph of the relation \(y = x^{2} - 2x - 5\); using a scale of 2 cm to 1 unit on the x- axis, and 2 cm to 2 units on the y- axis.
(c) Using the same axes, draw the graph of \(y = 2x + 3\).
(d) Obtain in the form \(ax^{2} + bx + c = 0\) where a, b and c are integers, the equation which is satisfied by the x- coordinate of the points of intersection of the two graphs.
(e) From your graphs, determine the roots of the equation obtained in (d) above.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
x
-3
-2
-1
0
1
2
3
4
5
\(x^{2}\)
9
4
1
0
1
4
9
16
25
\(-2x\)
6
4
2
0
-2
-4
-6
-8
-10
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
y
10
3
-2
-5
-6
-5
-2
3
10
(b) see graph above
(c)
x
-3
-2
-1
0
1
2
3
4
5
\(2x\)
-6
-4
-2
0
2
4
6
8
10
-3
-3
-3
-3
-3
-3
-3
-3
-3
-3
y
-9
-7
-5
-3
-1
1
3
5
7
(d) \(x^{2} - 2x - 5 = 2x - 3\)
\(x^{2} - 2x - 2x - 5 + 3 = 0\)
\(x^{2} - 4x - 2 = 0\)
(e) x = -0.8 or 4.3
Source: WAEC / JAMB / NECO Classroom Archive (Record #53477)