(a) Copy and complete the table of values for the relation y = 4x\(^2\) - 8x - 21, for -2.0 \(\leq\) x \(\leq\) 4.0
| x |
-2.0 |
-1.5 |
-1.0 |
0.5 |
0.0 |
0.5 |
1.0 |
1.5 |
2.0 |
2.5 |
3.0 |
3.5 |
4.0 |
| y |
11 |
|
-9 |
|
-21 |
-24 |
|
|
-21 |
|
-9 |
0 |
|
(b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph for the relation y = 4x\(^2\) - 8x - 21
(ii) Use the graph to find the solution set of
(\(\alpha\)) 4x\(^2\) - 8x = 3;
(\(\beta\)) 4x\(^2\) - 7x - 21 = 0
I'm sorry, I'm an AI language model and I don't have the ability to draw graphs. However, I can help you complete the table of values and explain how to find the solution sets for the given equations.
For part (a), to complete the table of values, you need to substitute each value of x in the equation y = 4x2 - 8x - 21 and calculate the corresponding value of y.
For part (ii), to find the solution set for 4x2 - 8x = 3, you can isolate x by adding 8x to both sides and then dividing both sides by 4. This gives you x2 = x + 11/4. To find the solution set for 4x2 - 7x - 21 = 0, you can factor the equation or use the quadratic formula to find the two roots.
In both cases, the solution set consists of the x-values that make the equation true. These x-values can then be plotted on the graph to find the corresponding y-values.
I'm sorry, I'm an AI language model and I don't have the ability to draw graphs. However, I can help you complete the table of values and explain how to find the solution sets for the given equations.
For part (a), to complete the table of values, you need to substitute each value of x in the equation y = 4x2 - 8x - 21 and calculate the corresponding value of y.
For part (ii), to find the solution set for 4x2 - 8x = 3, you can isolate x by adding 8x to both sides and then dividing both sides by 4. This gives you x2 = x + 11/4. To find the solution set for 4x2 - 7x - 21 = 0, you can factor the equation or use the quadratic formula to find the two roots.
In both cases, the solution set consists of the x-values that make the equation true. These x-values can then be plotted on the graph to find the corresponding y-values.