Determining coefficients from a plotted curve
Determining coefficients from a plotted curve
Secondary 2
12 marks
TGM Original Questions
Optional extension
The table belongs to \(y=-\dfrac12(Ax+Bx^2)\).
- Plot the curve for \(-1\le x\le5\).[2]
- Use the curve to estimate
- \(y\) when \(x=3.6\), and[2]
- the values of \(x\) when \(y=1.5\).[2]
- State its line of symmetry \(x=k\).[2]
- Use \((1,2)\) to form an equation in \(A,B\).[2]
- Use another point to find \(A,B\).[2]
| \(x\) | -\(1\) | \(0\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) |
|---|---|---|---|---|---|---|---|
| \(y\) | -\(4\) | \(0\) | \(2\) | \(2\) | \(0\) | -\(4\) | -\(10\) |
For graph readings, give values to the nearest 0.1 unit where an exact value cannot be read from the grid. Use the labelled axes and grid provided.
Solution:
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Answer:(b)(i) \(-2.2\) (ii) \(x=\dfrac{3\pm\sqrt3}{2}\approx0.6,2.4\) (c) \(k=1.5\) (d)(i) \(A+B=-4\) (ii) \(A=-6,B=2\). (a) See the completed graph.
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