Question 4.6: (a) Sketch the graph of y = 2x² – 7x – 9 for values of x fro......
(a) Sketch the graph of y = 2x² – 7x – 9 for values of x from –2 to 6.
(b) Calculate the points of intersection with the axes; hence, find the roots and mark the roots of 2x² − 7x − 9 on the diagram.
(c) Estimate the coordinates of the turning point from the graph.
(d) Measure the difference between the x-coordinate of the turning point and each root.
(a) Calculate the y-values given x, ranging from x = –2 to 6. The results are given in Table 4.3 and sketched in Figure 4.7.
(b) The points of intersection with the axes are calculated as follows:
- The graph cuts the y-axis when x = 0, that is, at y=−9.
- The graph cuts the x-axis at y = 0, that is, at 2x² − 7x − 9 = 0.
See the quadratic equation whose roots are x = –1 and x = 4.5. See Figure 4.6.
(c) From the graph the minimum point is at x = 1.75, y = –17 approximately. These points can be found exactly using differentiation in Chapter 6.
(d) The two roots are an equal distance, 2.75, on either side of the vertical line drawn through the minimum point.
| Table 4.3 Calculation of points for y = 2x² − 7x − 9 | |
| x | y |
| -2 | 13 |
| -1 | 0 |
| 0 | -9 |
| 1 | -14 |
| 2 | -15 |
| 3 | -12 |
| 4 | -5 |
| 5 | 6 |
| 6 | 12 |
