Determining coefficients from a plotted curve

Determining coefficients from a plotted curve

Secondary 2
TGM Original Questions

The table belongs to \(y=-\frac12(Ax+Bx^2)\).

  1. Plot the curve for \(-1\le x\le5\).
  2. Use the curve to estimate
    1. \(y\) when \(x=3.6\), and
    2. the values of \(x\) when \(y=1.5\).
  3. State its line of symmetry \(x=k\).
    1. Use \((1,2)\) to form an equation in \(A,B\).
    2. Use another point to find \(A,B\).
\(x\)-\(1\)\(0\)\(1\)\(2\)\(3\)\(4\)\(5\)
\(y\)-\(4\)\(0\)\(2\)\(2\)\(0\)-\(4\)-\(10\)

Solution:

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Answer:(b)(i) \(-2.16\); (ii) \(x=\frac{3\pm\sqrt3}{2}\approx0.63,2.37\); (c) \(k=1.5\); (d)(i) \(A+B=-4\); (ii) \(A=-6,B=2\).

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