Non-Linear Graphical Functions

Students learn how to  plot quadratic, cubic, reciprocal and exponential 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.


Non-Linear 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, plot and interpret graphs of quadratic functions, simple cubic functions and the reciprocal function y = 1/x with x ≠ 0.
  • Solve quadratic equations by finding approximate solutions using a graph
  • Plot and interpret graphs exponential graphs
  • Recognise and use the equation of a circle with centre at the origin
  • Find the equation of a tangent to a circle at a given point.


Key Concepts
  • To generate the coordinate’s 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 and therefore do not have straight lines. All graphs of this nature should be drawn with smooth curves.
  • When solving equations graphically students should realise solutions are only approximate.
  • Students need to gain an understanding of the shape of each function in order to identify incorrectly plotted coordinates.
  • The equation of a circle relates very closely to Pythagoras’ theorem.
  • Exponential graphs can be increasing as well as decreasing.
  • Students need to understand the equivalence between linear graphs in the form y = mx + c and ax + by + c = 0.

Common Misconceptions
  • Students often have difficulty substituting in negative values to complex equations. Encourage the use of mental arithmetic.
  • Identifying the correct type of function from graphs is often a source of confusion.
  • By creating the table of results students will be more able to choose a suitable scale for their axes.
  • Students who complete the table of results correctly often have little difficulty plotting the graph correctly.
  • Students often have difficulty drawing the equation of a circle correctly in examinations.
  • Students often have difficulty stating the equation of a linear graph in the form ax + by + c = 0.

 

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