Two automated precision sensors, A A\,A and BBB, track the vertical displacement y y\,y of a mechanical component as a function of its horizontal position x x\,x along a rail. The displacement recorded by sensor A A\,A is modelled by y=∣2x∣y = |2x|y=∣2x∣, and the displacement recorded by sensor B B\,B is modelled by y=∣5x−21∣y = |5x - 21|y=∣5x−21∣.
Sketch both graphs on the same set of axes. Clearly indicate the coordinates of the vertex of each graph and any point where the graphs intersect the yyy-axis.
Determine the coordinates of the points of intersection of the two graphs. Fully justify your answer using algebraic methods.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.