More than Just Lines on a Map: Best Practices for U.S Bike Routes
4. Family Of Curves pdf format
1. 22.4 Family of Curves.notebook September 23, 2008
Families of Polynomial Functions
Crystal pieces for a large chandelier are to be cut according to the design
shown. The graph shows how the design is created using polynomial
functions. What do all the functions have in common? How are they different?
How can you determine the equations that are used to create the design?
In this section, you will determine equations for a family of polynomial functions from a set of zeros.
Given additional information, you will determine an equation for a particular member of the family.
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2. 22.4 Family of Curves.notebook September 23, 2008
Investigate How are polynomial functions with the same zeros related?
1. a﴿ Examine each set of parabolas and the corresponding functions.
b﴿ Reflect How are the graphs of the functions in part a﴿ similar and how are they different?
2. Reflect Describe the relationship between the graphs of functions of the form y = k﴾x 1﴿﴾x + 2﴿, where
k ∈ R. Why do you think this is called a family of functions ?
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4. 22.4 Family of Curves.notebook September 23, 2008
Example 1 Represent a Family of Functions Algebraically
The zeros of a family of quadratic functions are 2 and 3.
a﴿ Determine an equation for this family of functions.
b﴿ Write equations for two functions that belong to this family.
c﴿ Determine an equation for the member of the family that passes through
the point ﴾1, 4﴿.
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5. 22.4 Family of Curves.notebook September 23, 2008
Example 2 Determine an Equation for a Family of Cubic Functions Given Integral Zeros
The zeros of a family of cubic functions are 2, 1, and 3.
a﴿ Determine an equation for this family.
b﴿ Write equations for two functions that belong to this family.
c﴿ Determine an equation for the member of the family whose graph has a
yintercept of 15.
d﴿ Sketch graphs of the functions in parts b﴿ and c﴿.
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6. 22.4 Family of Curves.notebook September 23, 2008
Determine an Equation for a Family of Quartic
Example 3
Functions Given Irrational Zeros
a﴿ Determine a simplified equation for the family of quartic functions with zeros ±1 and 2 ± √3 .
b﴿ Determine an equation for the member of the family whose graph passes through the point ﴾2, 18﴿.
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7. 22.4 Family of Curves.notebook September 23, 2008
Determine an Equation for a Quartic Function
Example 4
From a Graph
Determine an equation for the quartic function represented by this graph.
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