Graphical Functions

Students learn how to create and use a table of results to plot a quadratic, cubic and reciprocal graphs.  As learning progresses they use these graphs to model a range of scenerios and estimate solutions to equations.

This unit takes place in Term 5 of Year 10 and follows straight line graphs.


Graphical Functions Lessons


Prerequisite Knowledge
  • plot graphs of equations that correspond to straight-line graphs in the coordinate plane
  • recognise, sketch and interpret graphs of linear functions

Success Criteria
  • Recognise, sketch and interpret graphs of quadratic functions, simple cubic functions, the reciprocal function y = 1/x with x ≠ 0.
  • Solve quadratic equations by finding approximate solutions using a graph


Key Concepts
  • To generate the co-ordinates students need to have a secure understanding of applying the order of operations to substitute and evaluate known values into equations.
  • Quadratic, Cubic and Reciprocal functions are non-linear which means they do not have straight lines. All graphs of this nature should be drawn with smooth curves.
  • Students need to gain an understanding of the shape of each function in order to identify incorrectly plotted coordinates

Common Misconceptions
  • Students often have difficulty substituting in negative values to complex equations. Encourage the use of mental arithmetic.
  • By identifying lines of symmetry in each function students will have a greater understanding of the typical shapes for each function.
  • By creating the table of results students will be more able to choose a suitable scale for their axes.

 

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