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∣+kf(x) = |4x + 3k| + kf(x)=∣4x+3k∣+k
and 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 Edexcel A Level Maths Functions and Graphs with exam-style questions for A Level Maths. 100 questions covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems, matched to the Edexcel A Level Maths (9MA0) 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.