The curve with equation y=px2−4px−5py=px^2-4px-5py=px2−4px−5p, where p p,p is a constant, does not intersect the line with equation y=2x−12y=2x-12y=2x−12 when 4−79<p<4+79\displaystyle \frac{4-\sqrt{7}}{9}<p<\frac{4+\sqrt{7}}{9}94−7<p<94+7.
Show that 9p2−8p+1<09p^2-8p+1<09p2−8p+1<0.
Verify that the curve does not intersect the line.
322 exam-style questions on Edexcel A Level Maths Quadratics, covering 2.1 Solving Quadratics, 2.2 Completing the Square, 2.3 Sketching Quadratic Graphs, 2.4 The Discriminant, and 2.5 Modelling with Quadratics. Each one has a worked solution and a mark scheme showing where the marks go.