Quadratic Functions

Programme Outline

Jamie visits the Speed Skydiving World Cup to witness the techniques employed by the competitors in their efforts to complete the fastest free fall descent. Jamie introduces the quadratic function d = 5t², which would describe the relationship between the distance fallen and the time taken if there were no air resistance. He draws and interprets the graph of d = 5t².

Katie shows how d = 5t² is related to y = 5x². She completes a table for negative x values and plots points to extend the graph into the second quadrant. She explains how to recognise a quadratic function and introduces the term ‘parabola’.

Katie and Jamie are in Trafalgar Square to play ‘Spot the Quadratic’. A number of functions and their graphs are shown and the presenters describe how to recognise the quadratics.

Katie attends a gathering of the British Motorcycle Federation to meet the ‘Kangaroo Kid’. This stuntman specialises in jumping over cars, trucks, tractors and even aeroplanes, on his quad bike. We are introduced to a quadratic equation that models the relationship between height and distance over a typical jump (h = 0.05d – 0.01d²). By completing a table of values and drawing the graph, Katie is able to predict the maximum height and the distance travelled for this stunt.

In this week’s ‘Tick or Trash’ Jamie and Katie tackle completing a table of values and drawing a graph for the function y = 2x + x². Katie makes mistakes within her table and the effects of this on her graph are discussed.

Finally a ‘top tip’ is given to help students remember the link between the sign of the x² term and the orientation of the parabola.