Cliff trajectory graph

Cliff trajectory graph

Secondary 2
10 marks
TGM Original Questions

Optional extension

A stone’s height above sea level is \(y=45+12x-x^2\) metres after travelling \(x\) metres horizontally.

  1. complete the missing table values \(p,q\)[2]
  2. draw for \(0\le x\le12\)[2]
  3. find
    1. cliff height,[2]
    2. horizontal distance travelled while above \(77\) m[2]
  4. find greatest height.[2]
\(x\)\(0\)\(2\)\(4\)\(6\)\(8\)\(10\)\(12\)
\(y\)\(45\)\(65\)\(p\)\(81\)\(q\)\(65\)\(45\)

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) \(p=77,q=77\) (c)(i) \(45\) m (ii) \(4\) m (d) \(81\) m. (b) See the completed graph.

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