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Cubic Graphs

Graphs HOME | Achievement Objectives | Parabola Graphs | Parabola Questions | Cubics | Hyperbola | Circles | Exponential | Logs | Radians | Trig Graphs Overview | Trig Vertical Shift | Trig Horizontal Shift | Trig Equations | Trig Models | General Translations | Applications | Revision

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Cubic Functions & Graphs

Basic Cubic graph y = x3,
Translated Cubic using the turning point y = ±a(x ± c)2 ± d
Sketching factorised cubics y = ±a(x ± b)(x ± c)(x ± d)
and other forms eg. y = ±a(x ± b)(x ± c)2

Remember to define the Domain if you write the equation for part of a cubic graph.

Cubic Graphs (Allow macros on spreadsheets)

Class notes, Blank notes

Ex10.04

Cubics

p44,

GeoGebra Java Cubics | With Brackets

 

Jump down to... Basic cubic | inverted cubic | vertical shift  | horizontal shift | combined shifts | factorised cubics | vertical stretch

Basiccubic

Cubic rule

x y
3 27
2 8
1 1
0 0
-1 -1
-2 -8
-3 -27

Note the rotational symmetry about the point (0,0)

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Inverted cubic

A negative multiplier inverts the graph about the turning point
 

 

Mouse-over the equations to see the graph translation

 

Note: The turning point (0,0) remains unchanged

 

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Vertical shift

Adding a constant vertically translates the cubic graph

Mouse-over the equations to see the graph translation

Note: Translate the point (0,0) then sketch the graph from this point.

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Horizontal shift

Adding a constant to x horizontally translates the cubic graph

Mouse-over the equations to see the graph translation

Note: The translation is opposite to what you would expect

 

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Combined shifts

Horizontal and vertical shifts can be combined

Mouse-over the equations to see the graph translation

 

Note: Translate the turning point (0,0), then sketch the graph from this point

Excel demo (contains macros)

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Factored cubics

Find the x intercepts by making each bracket = 0
 

Find the y intercept by putting x = 0 in the equation

 

Mouse-over the equations to see the graph translation

 
Note: Mark the x intercepts and the y intercept.

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Vertical stretch

A multiplier stretches or compresses the graph vertically

 

Mouse-over the equations to see the graph translation

Note: The turning point (0,0) remains unchanged
Excel demo (contains macros)

 

Continue to hyperbola

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