(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...
Question 1 Report
(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
(\(\alpha\)) \(4x^2 - 8x = 3\);
(\(\beta\)) \(4x^2 - 7x - 21 = 0\)
Answer Details
(a) For the missing entry between rm x=-1.0 rm and rm x=0.0 rm , the intended value is rm x=-0.5 rm . The completed table is:
| 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 |
For example, when rm x=-1.5 rm ,
\[y=4(-1.5)^2-8(-1.5)-21=9+12-21=0.\]
(b)(i) The graph of rm y=4x^2-8x-21 rm is shown below. The plotted curve uses the stated scales: 2 cm represents 1 unit on the rm x rm -axis and 2 cm represents 5 units on the rm y rm -axis.
(b)(ii)( rm rm )
\[4x^2-8x=3\]
Since rm y=4x^2-8x-21 rm , this gives
\[y=3-21=-18.\]
From the intersections of the curve with the line rm y=-18 rm ,
\[\boxed{x\approx -0.35\quad\text{or}\quad x\approx2.3}.\]
(b)(ii)( rm rm )
\[4x^2-7x-21=0.\]
Writing this in terms of the plotted curve,
\[4x^2-8x-21=-x,\]
so draw the line rm y=-x rm . From its intersections with the curve,
\[\boxed{x\approx-1.6\quad\text{or}\quad x\approx3.3}.\]
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