(a) Copy and complete the table for \(y = 3x^{2} - 5x - 7\)
x
-3
-2
-1
0
1
2
3
4
\(y = 3x^{2} - 5x - 7\)
35
-7
-9
5
(b) Using a scale of 2cm = 1 unit along the x- axis and 2cm = 5 units along the y- axis, draw the graph of \(y = 3x^{2} - 5x - 7\). (c) On the same axis, draw the graph of \(y + 3x + 2 = 0\). (d) From your graph, find the : (i) range of values of x for which \(3x^{2} - 5x - 7 < 0\) ; (ii) roots of the equation \(3x^{2} - 2x - 5 = 0\).
Explanation
(a)
x
-3
-2
-1
0
1
2
3
4
\(y = 3x^{2} - 5x - 7\)
35
15
1
-7
-9
-5
5
21
(b) (c) \(y + 3x + 2 = 0 \implies y = -3x - 2\) when x = -2, y = 6 - 2 = 4. when x = 3, y = -9 - 2 = -11. (d) \(3x^{2} - 2x - 5 = 0 = 3x^{2} - 5x - 7 = -3x - 2\) The roots of the equation \(3x^{2} - 2x - 5 = 0\) is when the line \(y = -3x - 2\) cuts the equation i.e. x = 1.0 or 1.7.
