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.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.