(a) Copy and complete the table of values for the relation y=2x\(^2\) - x - 2 for 4 ≤ x ≤ 4.
(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 2x\(^2\) - x - 2 for 4 ≤ x ≤ 4.
(c) On the same axes, draw the graph of y = 2x + 3.
(d) Use the graph to find the: (i) roots of the equation 2x-3r-5 0; (i) range of values of x for which 2x\(^2\) -x - 2<0.
(a)
To complete the table of values for the relation y=2x\(^2\) - x - 2 for 4 ≤ x ≤ 4, we need to substitute each value of x into the equation and calculate the corresponding value of y.
| x |
-4 |
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
| y |
30 |
19 |
8 |
-1 |
-2 |
-1 |
4 |
13 |
26 |
(b)
Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, we can plot the points from the completed table of values to draw the graph of y = 2x\(^2\) - x - 2 for 4 ≤ x ≤ 4. The graph should be a smooth curve passing through the plotted points.
(c)
On the same axes, we can draw the graph of y = 2x + 3 by plotting some points and drawing a straight line passing through them. For example, when x = -2, y = -1, and when x = 2, y = 7. This gives us two points (-2,-1) and (2,7), which we can use to draw the line.
(d)
(i)
To find the roots of the equation 2x - 3r - 5 = 0 using the graph, we need to look for the points where the graph intersects the line y = 2x - 5. These points correspond to the values of x that satisfy the equation. From the graph, it appears that the intersection point is around x = 3. Therefore, we can estimate that the root of the equation is x ≈ 3.
(ii)
To find the range of values of x for which 2x\(^2\) -x - 2 < 0 using the graph, we need to look for the points where the graph is below the x-axis. These points correspond to the values of x that satisfy the inequality. From the graph, it appears that the graph is below the x-axis for values of x between approximately -1.5 and 1.5. Therefore, the range of values of x for which 2x\(^2\) -x - 2 < 0 is -1.5 < x < 1.5.