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1.5 B: Algebra and functions

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Question 254

A roller coaster engineer uses a polynomial function h(x)h(x)h(x) to model the height, in decametres, of a section of track relative to a horizontal distance xxx.

The function h(x)h(x)h(x) is defined for all x∈Rx \in \mathbb{R}x∈R. The profile of the track has the following features:

  • It touches the horizontal axis at a local minimum turning point at (2,0)(2, 0)(2,0).
  • It has a local maximum turning point at (−2,8)(-2, 8)(−2,8).
  • It crosses the vertical axis at the point (0,4)(0, 4)(0,4).
  • The graph behaves like a positive cubic, falling to the left and rising to the right.

On separate diagrams, sketch the curve with the following transformed equations:

i.

y=0.5h(x+2)y = 0.5h(x + 2)y=0.5h(x+2)

On each sketch, show clearly the coordinates of:

  • the point where the curve crosses the yyy-axis
  • any maximum or minimum turning points
[4]
ii.

y=h(2x)−5y = h(2x) - 5y=h(2x)−5

On each sketch, show clearly the coordinates of:

  • the point where the curve crosses the yyy-axis
  • any maximum or minimum turning points
[4]

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

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.

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