Intersections with a horizontal line

Intersections with a horizontal line

IP 2
5 marks
TGM Original Questions

A curve has equation \(y=(x-3)^2-4\).

  1. Find the x-coordinates where the curve meets the x-axis.[2]
  2. State the coordinates of the turning point.[1]
  3. Find all values of \(k\) for which the line \(y=k\) meets the curve at two distinct points. Explain your answer.[2]

Solution:

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Answer:(a) \(x=1\text{ or}\hspace{0.5em}x=5\) (b) \((3,-4)\) (c) \(k>-4\)

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