Quadratic Graph: Table of Values and Curve Sketching
Quadratic Graph: Table of Values and Curve Sketching
Secondary 2
Answer the whole of this question on a sheet of graph paper.
The variables \(x\) and \(y\) are connected by the equation \(y=4-3x-{{x}^{2}}\).
The table below shows some values of \(x\) and the corresponding values of \(y\).
| \(x\) | \(-4\) | \(-3\) | \(-2\) | \(-1\) | \(0\) | \(1\) | \(2\) |
|---|---|---|---|---|---|---|---|
| \(y\) | \(0\) | \(p\) | \(6\) | \(q\) | \(4\) | \(0\) | \(-6\) |
- Calculate the values of \(p\) and \(q\).
- Using a scale of \(2\) cm to represent \(1\) unit on the horizontal \(x\)-axis and \(1\) cm to represent \(1\) unit on the vertical \(y\)-axis, draw the graph of \(y=4-3x-{{x}^{2}}\) for \(-4\le x\le 2\).
- From the graph, find the
- values of \(x\) when \(y=3\),
- maximum value of \(y\).
- By drawing a suitable tangent, find the gradient of the graph at the point where \(x=-1\).
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Answer:(a) \(p=4\), \(q=6\) (b) Smooth curve through \((-4,0),(-3,4),(-2,6),(-1,6),(0,4),(1,0),(2,-6)\) (c)(i) \(x\approx-3.3\) or \(x\approx0.3\) (c)(ii) Maximum \(y\approx6.3\) (d) \(-1\)
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