Hyperbolas and Circles

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Hyperbolas and Circles

description

Hyperbolas and Circles. Learning Targets. To recognize and describe the characteristics of a hyperbola and circle. To relate the transformations, reflections and translations of a hyperbola and circle to an equation or graph. Hyperbola. - PowerPoint PPT Presentation

Transcript of Hyperbolas and Circles

Page 1: Hyperbolas and Circles

Hyperbolas and Circles

Page 2: Hyperbolas and Circles

Learning Targets

To recognize and describe the characteristics of a hyperbola and circle.

To relate the transformations, reflections and translations of a hyperbola and circle to an equation or graph

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Hyperbola

A hyperbola is also known as a rational function and is expressed as INSERT EQUATION

GRAPH

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Hyperbola Characteristics

Graph

The characteristics of a hyperbola are:• Has no vertical or

horizontal symmetry• There are both horizontal

and vertical asymptotes• The domain and range is

limited

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Locator Point

Graph

The locator point for this function is where the horizontal and vertical asymptotes intersect.

Therefore we use the origin, (0,0).

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Standard Form

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Impacts of h and k

Graph

Based on the graph at the right what inputs/outputs can our function never have?

This point is known as the hyperbolas ‘hole’

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Impacts of h and k

Graph

The coordinates of this hole are actually the values we cannot have in our domain and range.

Domain: all real numbers for x other than h

Range: all real numbers for y other than k

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Impacts of h and k

Graph

This also means that our asymptotes can be identified as:

Vertical Asymptote: x=h

Horizontal Asymptote: y=k

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Example #1

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Example #2

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Impacts of a

Graph

Our stretch/compression factor will once again change the shape of our function.

The multiple of the factor will will determine how close our graph is to the ‘hole’

The larger the a value, the further away our graph will be.

The smaller the a value , the closer our graph will be.

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Example #3

Graph

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Circle