Question 7
- Copy and complete the table of values for the equation y = 2x2 – 7x – 9 for -3 ≤ x ≤ 6.
X |
-3 |
- 2 |
-1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
Y |
|
13 |
|
-9 |
-14 |
|
-12 |
|
6 |
|
- Using scales of 2 cm to 1 unit on the x –axis and 2 cm to 4 units on the y – axis, draw the graph of y = 2x2 – 7x – 9 for -3 ≤ x ≤ 6.
- Use the graph to estimate the:
- roots of the equation 2x2 – 7x = 26;
(ii) coordinates of the minimum point of y;
(iii) range of values for which 2x2 – 7x < 9.
Observation
The Chief Examiner reported that majority of the Candidates’ who attempted this question got right the complete table of values for which y = 2x2 – 7x – 9. However, many failed to plot the points on the graph correctly on the graph thereby loosing marks. Also, they could not read up values from the graph to answer subsequent questions.
In part (a), the Candidates were expected to complete the table as follows:
X |
-3 |
- 2 |
-1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
Y |
30 |
13 |
0 |
-9 |
-14 |
-15 |
-12 |
-5 |
6 |
21 |
In part (b), Candidates would then use this table and the scale provided to draw the graph of the relation y = 2x2 – 7x – 9 and use this graph to answer the questions that followed.
In part (c), from the graph, the roots of the equation 2x2 – 7x = 26 were obtained by drawing a line through y = 17 to meet the curve y = 2x2 – 7x – 9. The required roots are – 2.2 ± 0.1 and 5.8 ± 0.1. The coordinates of the minimum point of y is 1.8 ± 0.1, -15 ± 0.4. The ranges -1
0.1<x<4.5
.1.