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

When drawing the graph of an equation, the roots of the equation are where its graph intercepts the x-axis (where y = 0).

The turning point of a graph is a point on the curve where, as x increases, the y values change from decreasing to increasing or vice versa.

Key features of a cubic graph

Maths

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.

Non-linear graphs

The point on the graph of a curve where, as $$x$$ increases, the $$y$$ values change from decreasing to increasing (or vice versa) is called the __________.

How many roots can the graph of a cubic equation have?

This is the graph of $$y=x^{3}-9x^{2}+24x-16$$. Which $$y$$ values make this statement true? $$y=x^{3}-9x^{2}+24x-16$$ has two solutions. 

This is the equation $$y=x^{3}-9x^{2}+24x-16$$. The root $$x=4$$ is a __________. 

The equation $$y=x^3-21x+20$$ factorises to $$y=(x-1)(x-4)(x+5)$$. What are the roots of the equation?

$$x=-5$$ and $$x=0$$ are two roots of $$y=x^3+2x^2-15x$$. The third root is $$x=$${{}}.

A cubic is an equation, graph, or sequence where the highest __________ of the variable is 3.

How many solutions can a quadratic equation have?

What is $$y$$-intercept of this quadratic graph?

What are the roots of this quadratic equation?

The point (3, -1) is the {{}} point of this quadratic curve.

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