The height of a drone path during a test flight is modeled by the function y=f(x)y = f(x)y=f(x), where
f(x)=∣4x+3k∣+k f(x) = |4x + 3k| + k f(x)=∣4x+3k∣+kand where kkk is a positive constant and xxx is the horizontal distance from a start point. The graph of y=f(x)y = f(x)y=f(x) has a vertex at the point PPP.
Find, in terms of kkk, the coordinates of PPP.
Sketch the graph with equation y=g(x)y = g(x)y=g(x), where g(x)=∣x−5k∣g(x) = |x - 5k|g(x)=∣x−5k∣. On your sketch, show the coordinates, in terms of kkk, of each point where the graph cuts or meets the coordinate axes.
The drone path with equation y=f(x)y = f(x)y=f(x) is monitored by a sensor following the path y=g(x)y = g(x)y=g(x). The paths intersect at two points.
Find, in terms of kkk, the coordinates of these two intersection points.
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.
