2026 HGV P2 Q1

2026 HGV P2 Q1

Secondary 4
4 marks
  1. Express \(3x^2-24x+58\) in the form \(a(x+b)^2+c\) where \(a\), \(b\) and \(c\) are constants.[3]
  2. Hence explain why there is no intersection between the graph \(y=3x^2-24x+58\) and the line \(y=9\).[1]

Solution:

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Answer:(a) \(3(x-4)^2+10\). (b) The curve has minimum \(y=10>9\), so there is no intersection.

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