(a) Copy and complete the table of values for the equation \(y = 2x^{2} - 7x - 9\) for \(-3 \leq x \leq 6\).
x
-3
-2
-1
0
1
2
3
4
5
6
y
13
-9
-14
-12
6
(b) Using scales of 2cm to 1 unit on the x- axis and 2cm to 4 units on the y- axis, draw the graphs of \(y = 2x^{2} - 7x - 9\) for \(-3 \leq x \leq 6\). (c) Use the graph to estimate the : (i) roots of the equation \(2x^{2} - 7x = 26\); (ii) coordinates of the minimum point of y; (iii) range of values for which \(2x^{2} - 7x < 9\).
Explanation
(a)
x
-3
-2
-1
0
1
2
3
4
5
6
y
30
13
0
-9
-14
-15
-12
-5
6
21
(b)
(c) (i) From the graph, the roots of the equation 2x\(^2\) - 7x = 26 can be obtained by drawing a line through y = 17 to meet the curve 2x\(^2\) - 7x - 9. The roots of the equation 2x\(^2\) - 7x = 26 : -2.2 and 5.8. (ii) The coordinates of the minimum point of y : 1.8, -15. (iii) The range of values for which 2x\(^{2}\) - 7x < 9 : - 0.9 < x < 4.5.
