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.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
