Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically
Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically
IP 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
- \(-3{{x}^{2}}+2x+8=-15\),
- \(-3{{x}^{2}}+2x+8=x+2\).
Solution:
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Answer:(a) \(a=-8\) (b) Graph shown in working (c)(i) \(x\approx-1.33\) or \(2\) (ii) Approximately \((0.33,8.33)\) (iii) \(x\approx0.33\) (d)(i) \(x\approx-2.46\) or \(3.12\) (ii) \(x\approx-1.26\) or \(1.59\)
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