Move a parallel line

7 written marks

The curve is \(y=x^2-x+6\) and the line is \(y=3x+c\).

1. Form the intersection equation and show that its discriminant is \(4(c-2)\).

   [2]

2. Classify all real \(c\) according to whether there are zero, one or two distinct real intersection points.

   [3]

3. Find the intersection points when \(c=6\).

   [2]

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