Quadratic Graph: Maximum Point, Values, and Symmetry
Quadratic Graph: Maximum Point, Values, and Symmetry
TGM Original
Answer the whole of this question on a sheet of graph paper.
The table below gives some \(x\) and \(y\) values of the equation \(y=-{{x}^{2}}-2x+5\).
| \(x\) | \(-4\) | \(-3\) | \(-2\) | \(-1\) | \(0\) | \(1\) | \(2\) | \(3\) |
|---|---|---|---|---|---|---|---|---|
| \(y\) | \(-3\) | \(2\) | \(5\) | \(6\) | \(5\) | \(2\) | \(-3\) | \(a\) |
- Find the value of \(a\).
- Taking \(2\)cm to represent \(1\) unit on the \(x\)-axis and \(1\) cm to represent \(1\) unit on the \(y\)-axis, draw the graph of \(y=-{{x}^{2}}-2x+5\) for \(-4\le x\le 3\).
- Use your graph to find
- the coordinates of the maximum point,
- the value of \(y\) when \(x=-1.5\),
- the values of \(x\) when \(y=4\),
- the equation of the line of symmetry.
- By drawing a suitable line, find the solutions to the equations
- \(-{{x}^{2}}-2x-3=0\),
- \(-{{x}^{2}}-x+7=0\).
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Answer:(a) \(a=-10\) (b) Graph of \(y=-x^2-2x+5\) for \(-4\leq x\leq3\) (c)(i) \((-1,6)\) (c)(ii) \(y\approx5.8\) (c)(iii) \(x\approx-2.4\) or \(0.4\) (c)(iv) \(x=-1\) (d)(i) No real solutions (d)(ii) \(x\approx-3.2\) or \(2.2\)
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