Non-Linear Graphical Functions

Plotting Quadratic Equations

Solving Quadratics Graphically

Plotting Cubic Equations

Plotting Reciprocal Functions

Plotting Exponential Graphs

Solving Equations Graphically

Equation of Circular Functions

Deriving the Equation of Tangents

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.