Graphical Functions

Plotting Quadratic Equations

Solving Quadratics Graphically

Plotting Cubic Equations

Plotting Reciprocal Functions

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.