(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...
Assessment:WAEC SSCE - General Mathematics - 2000 (Essay)Subject:General Mathematics
(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.
(a) Completing the table for \(y=x^2-2x-5\). For example, when \(x=-3\), \(y=9+6-5=10\), and when \(x=2\), \(y=4-4-5=-5\).
x
-3
-2
-1
0
1
2
3
4
5
y
10
3
-2
-5
-6
-5
-2
3
10
(b) and (c) The plotted curve is the parabola \(y=x^2-2x-5\). The straight line is \(y=2x+3\), which passes through \((0,3)\) and \((3,9)\).
(d) At a point of intersection, both graphs have the same \(y\)-value:
\[
x^2-2x-5=2x+3
\]
\[
x^2-4x-8=0
\]
(e) The roots are the \(x\)-coordinates of the intersections. From the graph, they are approximately \(x=-1.5\) and \(x=5.5\).
The more accurate solutions are \(x=2\pm2\sqrt{3}\), giving \(x\approx-1.46\) and \(x\approx5.46\). The supplied reference answer uses \(y=2x-3\), but this conflicts with the question stem, which states \(y=2x+3\). Therefore \(x^2-4x-8=0\) is the equation consistent with the stated line.
(a) Completing the table for \(y=x^2-2x-5\). For example, when \(x=-3\), \(y=9+6-5=10\), and when \(x=2\), \(y=4-4-5=-5\).
x
-3
-2
-1
0
1
2
3
4
5
y
10
3
-2
-5
-6
-5
-2
3
10
(b) and (c) The plotted curve is the parabola \(y=x^2-2x-5\). The straight line is \(y=2x+3\), which passes through \((0,3)\) and \((3,9)\).
(d) At a point of intersection, both graphs have the same \(y\)-value:
\[
x^2-2x-5=2x+3
\]
\[
x^2-4x-8=0
\]
(e) The roots are the \(x\)-coordinates of the intersections. From the graph, they are approximately \(x=-1.5\) and \(x=5.5\).
The more accurate solutions are \(x=2\pm2\sqrt{3}\), giving \(x\approx-1.46\) and \(x\approx5.46\). The supplied reference answer uses \(y=2x-3\), but this conflicts with the question stem, which states \(y=2x+3\). Therefore \(x^2-4x-8=0\) is the equation consistent with the stated line.