Nayland College

Nayland College - Mathematics

Home . Year 9 . Year 10 . Level 1 . Level 2 . L3 Statistics . L3 Maths . L3 Calculus . About . Links

NZAMT NZQA NZ Grapher NZ Maths Census at School Study It Khan Academy Desmos

Graphing Hyperbolas

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

4



Hyperbolas

Simple Hyperbola, in the form y = A/x and y = A/Bx
Graph asymptotes, shape and features (symmetry)

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

AND define the 'x' value not defined for the vertical asymptote eg x ≠3

 Hyperbola Graphs

  

Class notes, Blank notes | Daves notes | Worksheet

Ex11.01

Hyperbola

p45,

GeoGebra Java Hyperbola

5



Translated Hyperbola

Sketching hyperbolas in the form y = A/(x+B) + C
Finding both intercepts, asymptotes & sketching translated hyperbola

Class notes, Blank notes

Ex11.02, Ex11.03

p46, p47

 

Jump down to... Basic Hyperbola | hyperbola family | inverted hyperbola | vertical shift | horizontal shift | combined shifts

Basic hyperbola

Two numbers multiply to give a result of 3

Hyperbola rule

Features

Mouse-over the equations and key words to see the graph

x y
3 1
2 1.5
1 3
0 ?
-1 -3
-2 -1.5
-3 -1

FEATURES: Symmetry, asymptotes, no value at x = 0 or y = 0

NOTE: the asymptotes should be DOTTED

back to top

 

 

Hyperbola family

Changing the constant on the top of the equation
 

Mouse-over the equations and key words to see the graph

  Features

  Features
  Features
  Features

back to top

 

 

Inverted hyperbola

A negative multiplier inverts the graph about the horizontal asymptote
 

 

Mouse-over the equations and key words to see the graph

Features
 

back to top

 

 

Vertical shift

Adding a constant vertically translates the hyperbola graph
 

 

Mouse-over the equations and key words to see the graph

  Features
  Features
  Features

NOTE: A dotted asymptotes should be marked

back to top

 

 

Horizontal shift

Adding a constant to x horizontally translates the hyperbola graph
 

 

Mouse-over the equations and key words to see the graph


NOTE: the asymptote should be DOTTED

  Features
  Features
  Features

NOTE: A dotted vertical asymptote should be marked

back to top

 

 

Combined shifts

Horizontal and vertical shifts can be combined
 

 

Mouse-over the equations and key words to see the graph

Features


NOTE: the asymptotes should be DOTTED

Features

Features

 

NOTE: A dotted horizontal & vertical asymptote should be marked

Excel demo (contains macros)

 

Continue to circles

back to top