Comparing vertical stretches of a parabola

Comparing vertical stretches of a parabola

Secondary 2
6 marks
TGM Original Questions

Optional extension

The graph of \(y=x^2-9\) is shown.

  1. State its line of symmetry.[2]
  2. State its \(x\)-intercepts.[2]
  3. On the same axes, sketch and label \(y=3x^2-9\) and \(y=\dfrac13x^2-9\), showing how each compares with the given graph.[2]

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Answer:(a) \(x=0\) (b) \((-3,0),(3,0)\). (c) \(y=3x^2-9\) is narrower with roots \(x=\pm\sqrt3\); \(y=\dfrac13x^2-9\) is wider with roots \(x=\pm3\sqrt3\).

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