Symmetric paired points on a parabola

Symmetric paired points on a parabola

Secondary 2
12 marks
TGM Original Questions

Optional extension

For \(y=\dfrac15(15x-x^2)\):

  1. find missing table value \(p\)[2]
  2. draw the graph for \(0\le x\le15\)[2]
  3. The distinct points \((4,k)\) and \((h,k)\) lie on the curve. Find
    1. \(k\),[2]
    2. \(h\)[2]
  4. solve \(\dfrac15(15x-x^2)=0\)[2]
  5. state the maximum value.[2]
\(x\)\(0\)\(2\)\(4\)\(6\)\(8\)\(10\)\(12\)\(14\)\(15\)
\(y\)\(0\)\(5.2\)\(8.8\)\(10.8\)\(p\)\(10\)\(7.2\)\(2.8\)\(0\)

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:(a) \(p=11.2\) (c)(i) \(k=8.8\) (ii) \(h=11\) (d) \(x=0,15\) (e) \(11.25\). (b) See the completed graph.

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