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Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Bell WorkFind something to grade with
Going around in Circles
Review your work from “The Other Gap”
We will select one member of each group to share with the class what approaches they have tried.
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Symmetry…• The orchard is symmetrical…really all we have to consider is these two gaps. All other gaps are idencal to one of these two.
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
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October 17, 2012
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
(0,0)
(3,1)
(1 1/2, 1/2)
(1,0)
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Defining Circles Discussion• #1 ‐
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October 17, 2012
Defining Circles Discussion• #2 ‐
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Defining Circles Discussion• #3
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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• #4
Defining Circles Discussion
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Equaon of a Circle Centered at (a,b)
A Circle is the set of all points a given distance (radius) from a given point (center).
Equaon…
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Center Radius Form…Center – (7, 5) Radius – 9
Center – (11, ‐6) Radius – 3
Center – (‐4, ½) Radius – 9/5
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Review…• Find “c” so that the quadrac expression could be
wrien as a perfect square in the form
•
• This is called compleng the square!
x2 + 6x + c (x + ?)2
x2 12x + c (x ?)2
x2 + 13x + c (x + ?)2
x2 4/3x + c (x + ?)2
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Different Forms of the equaon• Can we write
in standard form?
• Could we reverse this process?
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Reverse the ProcessWhat if we started with
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Work• Move constant to
the other side
• Complete both squares AND add extra values to other side
• Rewrite using perfect square notaon
• Idenfy Center and Radius
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Group Pracce…• Complete the square to rewrite each of the following equaons Center Radius Form
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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October 17, 2012
Individual Pracce…
Orchard 20 Block 20 Other Gap Discussion_transforming circle eq.notebook
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Homework‐ POW Due 10‐23‐12
‐ Read pages 51‐52
‐ Complete Equaons of Circles WS
Tangent to a circle = only touches at one point