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.