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.
566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.