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 \(y=-\dfrac12(Ax+Bx^2)\).

  1. Plot the curve for \(-1\le x\le5\).[2]
  2. Use the curve to estimate
    1. \(y\) when \(x=3.6\), and[2]
    2. the values of \(x\) when \(y=1.5\).[2]
  3. State its line of symmetry \(x=k\).[2]
    1. Use \((1,2)\) to form an equation in \(A,B\).[2]
    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.

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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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