A curve has equation y=2(x−p)2−8y=2(x-p)^2-8y=2(x−p)2−8, where p p\,p is a constant, and its minimum point has xxx-coordinate 3.
State the value of p p\,p and the coordinates of the minimum point.
Find the exact coordinates of the points where the curve meets the xxx-axis.
33 exam-style questions on OCR (MEI) A Level Maths 1.4 Graphs, covering 1.4.1 Graphs of functions, 1.4.2 Intersection points with axes, 1.4.3 Completing the square for a quadratic curve, 1.4.4 Sketch graphs of simple functions, 1.4.5 Stationary points when curve sketching, 1.4.6 Graphs of reciprocal-type functions, 1.4.7 Single transformations of graphs, 1.4.8 Combined transformations of graphs (A-level only), and 1.4.9 Stationary points of inflection (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.