Mathematics 9709 · AS & A Level · Quadratics

Quadratics — practice question

The curve is given by $y = 2x^2 - 3x + 1$ and the line is given by $y = kx + k^2$, where $k$ is a constant.

(i)[4]

Demonstrate that, for every value of $k$, the curve and the line intersect.

(ii)[4]

State the value of $k$ for which the line is a tangent to the curve and determine the coordinates of the point at which the line touches the curve.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Clear use of the discriminant $b^2-4ac$.” …