CAIE P1 2018 November — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2018
SessionNovember
TopicInequalities

9 A curve has equation \(y = 2 x ^ { 2 } - 3 x + 1\) and a line has equation \(y = k x + k ^ { 2 }\), where \(k\) is a constant.
  1. Show that, for all values of \(k\), the curve and the line meet.
  2. State the value of \(k\) for which the line is a tangent to the curve and find the coordinates of the point where the line touches the curve.