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

Drawing cubic graphs

Maths

Checking and securing understanding of drawing quadratic graphs

Key features of a quadratic graph

Key features of a cubic graph

Drawing reciprocal graphs

Key features of a reciprocal graph

Drawing exponential graphs

Key features of an exponential graph

Drawing the graph for the equation of a circle

Advanced problem solving with non-linear 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

Which $$y$$ value is incorrect in this table of values for the equation $$y=x^3-9$$? Use a calculator.

What is the $$y$$ value when $$x=-3$$ for the equation $$y=12-x^3$$? Do not use a calculator for this question.

The diagram shows the graph of a cubic of the form $$y=ax^3+d$$. Which of these statements are correct?

Which of these will be $$y$$ values in this table for the equation $$x^{3}-5x^{2}+3x-4$$? Use a calculator.

In the equation $$y=5x^3-7$$, the $$3$$ is the __________ of $$x$$.

What is the value of $$x^3$$ when $$x=4$$?

What is the value of $$x^3$$ when $$x=-2$$?

Match each $$x$$ value to its corresponding $$y$$ value for the equation $$y=x^3-2$$.

Where is the $$y$$-intercept of the equation $$y=x^2-7x+8$$?

 Use a calculator to find the $$y$$ value when $$x=4$$ in the equation $$y=x^{3}-3x^{2}+2x$$. 

Drawing cubic graphs

Lesson outcome