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Quadratic Functions Teachers' Notes
The programme focuses on the nature of quadratic functions and graphs and is intended to provide enrichment and context alongside other teaching on this topic. Factorisation and other algebraic techniques are not covered. It is assumed that students will have encountered expressions containing squares prior to viewing and will be familiar with the substitution of values (including negative numbers) to generate a graph. Evaluating terms like 3x2 could be revised prior to viewing. The programme could be used as a revision tool or as an introduction to more detailed work on graphs. Some students may benefit from viewing short sections as they progress through stages of the work and then view the entire programme to summarise the main points. The equation used for the free fall speed skydiving is based on the equation of motion s = ut + ½at2,
taking u = 0 and g = 10m/s2. As stated in the programme, this assumes air resistance to be zero and the value found indicates the optimum time for completion of the racing kilometre. The equation for the quad bike jump was h = 0.05d – 0.01d2. This is based on projectile motion and again represents a simplification of the true situation. The functions and their graphs compared in Trafalgar Square were: y = 2x2 + 5x – 3
y = 3x – 4
y = x3 + 3x2 – 4x
y = 6 + ½x2
y = 5 – x2
Students could construct tables and plot graphs for these functions after viewing the programme. In addition, the answers to Worksheet 1 could form the basis of a discussion of the programme content.
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