The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2

A cubic is an equation, graph, or sequence whereby the highest exponent of the variable is 3

Problem solving with non-linear graphs

Maths

Checking and securing understanding of drawing quadratic graphs

Key features of a quadratic graph

Drawing cubic graphs

Drawing reciprocal graphs

In this unit, pupils consider other types of graphs. In the future unit, pupils consider different types of sequences such as Fibonacci and oscillating. Their knowledge is consolidated by linking all prior learning together.

In the prior unit, pupils studied the graphical representation of a geometric sequence and linked features of the graph to its equation. In this unit, other types of graphs are introduced and their key features identified.

In this unit graphical representations of non-linear graphs are introduced and explored, and their key features identified.

Non-linear graphs

The graph of $$y=x^3+2$$ will form a __________.

Which of these could be the equation of this graph?

Which of these equations could this graph represent?

Given that water is added at a steady rate which vase would generate this Depth-Time graph?

For this linear graph $$y=4x-3$$, the coordinates (0, -3) is the __________. 

$$y=4x-3$$ is a linear equation which therefore forms a __________ graph.

Izzy plots the graph of $$y=x^2$$. When the $$x$$ coordinate is $$-4$$, the $$y$$ coordinate is {{ }}.  

Jacob plots the graph of $$y=x^3$$. When the $$x$$ coordinate is $$-2$$, the $$y$$ coordinate is {{ }}.  

Sofia plots the reciprocal graph $$y={1\over{x}}$$. Which of these will be coordinate pairs?

This graph represents __________ of distance with respect to time.

Problem solving with non-linear graphs

Lesson outcome