(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
Explanation
(a) They completed the table of values as shown
| 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 | 0 | -9 | -16 | -21 | -24 | -25 | -24 | -21 | -16 | -9 | 0 | 11 |
(b)(i) The graph
(b)(ii)((alpha), deduce that 4x(^2) – 8x – 21 = 3 – 21 so that y = -18. From the graph, the point of intersection of y = -18 and y = 4x(^2) – 8x – 21 was atx = {-0.35 (pm) 0.1, 2.3 (pm) 0.1}
(b)(ii)((beta)), the equation 4x(^2) – 8x – 21 = 0 which can be written as 4x(^2) – x – 7x – 21 = -x. This implies that 4x(^2) – 8x – 21 = -x.
But, y = 4x(^2) – 8x – 21 so that y = -x, Next was to draw the line y = -x and from the graph, the point of intersection with the curve y = 4x(^2) – 8x – 21 was at x = {3.3 (pm) 0.1, -1.6 (pm) 0.1}