QUESTION 6
- Copy and complete the table of values for the relation y = 3x2 – x – 11, for -3 ≤ x ≤ 3.
x |
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |
y |
|
3 |
-7 |
|
|
|
|
- Using scales of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph of y = 3x2 – x – 11, for -3 ≤ x ≤ 3.
- Use the graph to find the:
- roots of 3x2 – x – 11 = 0;
- minimum value of y;
- gradient of the curve at the point x = 1.
Observation
The Chief Examiner reported that majority of the Candidates’ completed the table and also drew the graphs correctly but were unable to provide answers to part (c) fully.
In part (a), they did as expected by copying and completing the table of values as follows:
x |
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |
y |
19 |
3 |
-7 |
-11 |
-9 |
-1 |
13 |
In part (b), the graph was plotted as
In part (c), they were only able to read up the roots of roots of 3x2 – x – 11 = 0, which is
x = 
1.8 or 2.1 (
0.1) while in (c ii), they read the minimum value of y to be y = 
11.25 (
0.25)
but they had difficulty in finding the gradient at x = 1. The gradient from the graph is gradient = 4.5 (
0.5).