A surveyor models the profile of a heavy suspension cable using the function H(x)=4∣x−5∣+12H(x) = 4|x - 5| + 12H(x)=4∣x−5∣+12, where H H\,H is the vertical clearance in metres above a reference line and x x\,x is the horizontal distance in metres from a support pillar. The point V V\,V represents the lowest point of the cable profile.
State the coordinates of VVV.
Use algebra to determine the set of values of x x\,x for which
4∣x−5∣+12>6x 4|x - 5| + 12 > 6x 4∣x−5∣+12>6x(Solutions relying on calculator technology are not acceptable.)
The support pillar is moved and the cable tension is adjusted such that the profile is transformed to the graph with equation y=12H(x−2)\displaystyle y = \frac{1}{2}H(x - 2)y=21H(x−2). Find the new coordinates of VVV.
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.
