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Parabola 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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Overview & Parabolas

Unit Overview. Parabola sketching & transformations
Translation of the turning point y = ±a(x ± c)2 ± d
Sketching factorised parabolas y = ±a(x ± b)(x ± c)
Going from a graph to/from an equation

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

Parabola Transformations (Allow macros on spreadsheets)

Achievement Standard | Unit Overview | Parabola Class Notes | Blank Notes

Ex10.01, Ex10.02

Parabolas

p41, p42

GeoGebra Java Parabola Translation | Parabola Brackets

Jump down to... Basic parabola | inverted parabola | vertical shift | horizontal shift | combined shifts | factorised quadratics | vertical stretch | applications | Revision Questions | Excel graph demo (contains macros)

NOTE: this page contains "mouse over" graph changes.
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Basic parabola

Square each x value to get y

Remember a negative squares to give a positive

(mouse-over to see the graph change)

Quadratic rule
x y
3 9
2 4
1 1
0 0
-1 1
-2 4
-3 9

Note: The symmetry of the graph

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Inverted parabola

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 parabola graph

Mouse-over the equations to see the graph translation

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

 

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Horizontal shift

Adding a constant to x horizontally translates the parabola 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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Factorised quadratics

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 two x intercepts and the y intercept.
To find the coordinates of the turning point substitute the x value half way between the x intercepts into the equation to find the y value

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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
Excel graph demo (contains macros)
Continue to Parabola Questions

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