(a) Copy and complete the table of values for the relation \(y = 5 - 7x - 6x^{2}\) for \(-3 \leq x \leq 2\). x -3 -2 -1 -0.5 0 1 2 y -28 6 5 (b) Using a sca...
Question 1 Report
(a) Copy and complete the table of values for the relation \(y = 5 - 7x - 6x^{2}\) for \(-3 \leq x \leq 2\).
| x | -3 | -2 | -1 | -0.5 | 0 | 1 | 2 |
| y | -28 | 6 | 5 |
(b) Using a scale of 2cm to 1 unit on the x- axis and 2cm to 5 units on the y- axis, draw the :
(i) graph of \(y = 5 - 7x - 6x^{2}\) ; (ii) line \(y = 3\) on the same axis.
(c) Use your graph to find the : (i) roots of the equation \(2 - 7x - 6x^{2} = 0\) ; (ii) maximum value of \(y = 5 - 7x - 6x^{2}\).
Answer Details
(a) For \(y=5-7x-6x^2\), the completed table is:
| \(x\) | \(-3\) | \(-2\) | \(-1\) | \(-0.5\) | \(0\) | \(1\) | \(2\) |
|---|---|---|---|---|---|---|---|
| \(y=5-7x-6x^2\) | \(-28\) | \(-5\) | \(6\) | \(7\) | \(5\) | \(-8\) | \(-33\) |
(b) The required graph of \(y=5-7x-6x^2\) and the line \(y=3\) are shown below. The plotted points from the table lie on the smooth curve.
(c)(i) The roots of \(2-7x-6x^2=0\) are obtained by writing
\[2-7x-6x^2=0\iff 5-7x-6x^2=3.\]
Thus, they are the \(x\)-coordinates where the curve meets \(y=3\). Reading from the graph gives
\[\boxed{x\approx-1.4\text{ or }x\approx0.2}.\]
(c)(ii) The highest point of the curve is approximately \(7\) units. Hence,
\[\boxed{\text{Maximum value of }y=7\text{ (approximately)}}.\]
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