Quadratic Graph: Table of Values, Turning Point, and Symmetry
Quadratic Graph: Table of Values, Turning Point, and Symmetry
Secondary 2
Answer the whole of this question on a sheet of graph paper.
The variables \(x\) and \(y\) are connected by the equation \(y=-3{{x}^{2}}+2x+8\).
Some corresponding values are given in the following table.
| \(x\) | \(-3\) | \(-2\) | \(-1\) | \(0\) | \(1\) | \(2\) | \(3\) | \(4\) |
|---|---|---|---|---|---|---|---|---|
| \(y\) | \(-25\) | \({a}\) | \(3\) | \(8\) | \(7\) | \(0\) | \(-13\) | \(-32\) |
- Calculate the value of \(a\).
- Using a scale of \(2\) cm to represent \(1\) unit on the \(x\)-axis and \(2\) cm to represent \(5\) units on the \(y\)-axis, draw the graph of \(y=-3{{x}^{2}}+2x+8\) for \(-3\le x\le 4\).
- Using your graph, find the
- solutions to the equation \(-3{{x}^{2}}+2x+8=0\),
- coordinates of the turning point,
- the equation of the line of symmetry.
- By drawing a suitable line, find the solutions to the equations
- \(-3{{x}^{2}}+2x+8=-15\),
- \(-3{{x}^{2}}+2x+8=x+2\).
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Answer:(a) \(a=-8\) (b) Graph of \(y=-3x^2+2x+8\) for \(-3\leq x\leq4\) (c)(i) \(x=-\frac43\) or \(2\) (c)(ii) \(\left(\frac13,\frac{25}{3}\right)\) (c)(iii) \(x=\frac13\) (d)(i) \(x\approx-2.5\) or \(3.1\) (d)(ii) \(x\approx-1.3\) or \(1.6\)
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