Quadratic always positive/negative

Find parameter values ensuring a quadratic expression is always positive or always negative for all x, using discriminant or completing the square.

1 questions · Standard +0.3

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CAIE P1 2023 June Q2

4 marks Standard +0.3

2 The function f is defined for \(x \in \mathbb { R }\) by \(\mathrm { f } ( x ) = x ^ { 2 } - 6 x + c\), where \(c\) is a constant. It is given that \(\mathrm { f } ( x ) > 2\) for all values of \(x\). Find the set of possible values of \(c\).