Tangent to curve: find parameter

A question is this type if and only if it requires finding a constant (like k or m) such that a given line is tangent to a quadratic curve, typically using discriminant = 0.

1 questions · Standard +0.3

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Pre-U Pre-U 9794/2 2018 June Q2
11 marks Standard +0.3
2
  1. Express \(2 x ^ { 2 } + 6 x + 5\) in the form \(p ( x + q ) ^ { 2 } + r\).
  2. State the equation of the line of symmetry of the curve \(y = 2 x ^ { 2 } + 6 x + 5\).
  3. Find the value of the constant \(k\) for which the line \(y = k - 2 x\) is a tangent to the curve \(y = 2 x ^ { 2 } + 6 x + 5\).