Quadratic Functions | Cambridge O Level Additional Maths Topic Questions 2025

1

5 marks

Find the values of the constant $k$ for which the equation $(2 k - 1) x^{2} + 6 x + k + 1 = 0$ has real roots.

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1a

2 marks

Write the expression $x^{2} - 6 x + 1$ in the form ${(x + a)}^{2} + b$ , where $a$ and $b$ are constants.

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1b

1 mark

Hence write down the coordinates of the minimum point on the curve $y = x^{2} - 6 x + 1$ .

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1

5 marks

Find the values of $k$ for which the line $y = k x + 3$ is a tangent to the curve $y = 2 x^{2} + 4 x + k - 1$ .

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Quadratic Functions (Cambridge O Level Additional Maths)