Graphical Solution of Quadratic Function
Graphical Solution of Quadratic Function
TGM Original
Answer the whole of this question on a sheet of graph paper.
Copy and complete the following table of values for \(y=25+4x-2{{x}^{2}}\).
\(x\) | \(-3\) | \(-2\) | \(-1\) | \(0\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) |
|---|---|---|---|---|---|---|---|---|---|
\(y\) | \(-5\) | \(9\) | \(a\) | \(25\) | \(27\) | \(25\) | \(19\) | \(9\) | \(-5\) |
- Find 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 \(y=25+4x-2{{x}^{2}}\).
- Use your graph to estimate the solutions for the equation \(25+4x-2{{x}^{2}}=0\).
- By drawing a suitable straight line, estimate the solutions for the equation
- \(25+4x-2{{x}^{2}}=17.5\),
- \(25+4x-2{{x}^{2}}=-3\).
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Answer:(a) \(19\). (c) \(x\approx-2.67,4.67\). (d)(i) \(-1.18,3.18\); (ii) \(-2.87,4.87\).
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