use the resources on the internet and each other to help you relearn the concept. use whiteboards....
TRANSCRIPT
Opener
Use the resources on the internet and each other to help you relearn the concept.
Use whiteboards.Use laptops.Work together.
Opener - Solutions How well were you able to answer the question?
We will be reviewing our previous assignment next. So have your questions ready.
2.5 Writing a Polynomial Function SWBAT write a polynomial function
given the real and complex zeros.
Write down the date, Section #, Title and Learning Objective(s) into your notebook.
Key ConceptsLOOK LISTEN
Write down what you want into “Key Concepts” as you Look & Listen.
Complex Number Factoids:
1 i 2 1i
2 2( )( )a bi a bi a b
Difference of Squares:2 2( )( )a b a b a b
2 2x a b x a b x a b
Key ConceptsLOOK LISTEN
Write down what you want into “Key Concepts” as you Look & Listen.
Linear Factorization Theorem
If f(x) is a polynomial of degree n where n>0, f has precisely n linear factors.
1 2( ) n nf x a x c x c x c K
Where c1, c2, … cn are complex numbers.
Key ConceptsLOOK LISTEN
Write down what you want into “Key Concepts” as you Look & Listen.
Linear Factorization Theorem Example
2( ) 6 9f x x x
• This is a second degree polynomial and therefore must have precisely 2 complex zeros.
( ) ( 3)( 3)f x x x • After factoring, we can see that the zero is 3 and is
repeated twice. i.e. it has a multiplicity of 2.How would the graph intersect at this zero? How do you know?
Key ConceptsLOOK LISTEN
Write down what you want into “Key Concepts” as you Look & Listen.
Linear Factorization Theorem Example
3( ) 4f x x x
• This is a second degree polynomial and therefore must have precisely 3 complex zeros.
( ) ( 2 )( 2 )f x x x i x i • After factoring, we can see that the zeros are
{0, +2i, -2i}. How many intersection points would the graph have on the x-axis? Why?
Key ConceptsLOOK LISTEN
Write down what you want into “Key Concepts” as you Look & Listen.
If I am given the zeros, how do I find the polynomial?
Take each zero and replace in the “Linear Factorization Theorem.”
1 2( ) nf x x xc cc x K
How do we get there?
SWBAT write a polynomial function given the real & complex zeros.
LOOK LISTEN
Find a 2nd degree polynomial that has the given zeros of: {-4, 7}.
Now let’s try together.Use whiteboards.
SWBAT write a polynomial function given the real & complex zeros.
Find a 3rd degree polynomial that has the given zeros of: {0, 1, -2}.
Now let’s try together.Use whiteboards.
SWBAT write a polynomial function given the real & complex zeros.
Find a 2nd degree polynomial that has the given zeros of: {-5 with multiplicity of 2}.
Now you try.Write in notebook.
SWBAT write a polynomial function given the real & complex zeros.
Find a 3rd degree polynomial that has the given zeros of: {0 with multiplicity of 2, -1}.
How do we get there?LOOK LISTEN
SWBAT write a polynomial function given the real & complex zeros.
Find a 2nd degree polynomial that has the given zeros of: .{ }i
* Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.
Now let’s try together.Use whiteboards.
SWBAT write a polynomial function given the real & complex zeros.
Find a 4th degree polynomial that has the given zeros of: .{ 1,2, 3 }i
* Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.
Now let’s try together.Use whiteboards.
SWBAT write a polynomial function given the real & complex zeros.
Find a 3rd degree polynomial that has the given zeros of: .{ 1, 3, 3}
* Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.
Now let’s try together.Use whiteboards.
SWBAT write a polynomial function given the real & complex zeros.
Find a 5th degree polynomial that has the given zeros of: .{ 4,0,2,1 }i
* Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.
Now you try.Write in notebook.
SWBAT write a polynomial function given the real & complex zeros.
Find a 4th degree polynomial that has the given zeros of: .{ 1,0, , }i i
Now you try.Write in notebook.
SWBAT write a polynomial function given the real & complex zeros.
Find a 2nd degree polynomial that has the given zeros of: .{ 2, 2}
Now you try.Write in notebook.
SWBAT write a polynomial function given the real & complex zeros.
Find a 4th degree polynomial that has the given zeros of: .{ 1,2, 3 }i
Now you try.Write in notebook.
SWBAT write a polynomial function given the real & complex zeros.
Find a 4th degree polynomial that has the given zeros of: .{5, 5,4 }i
Now you try.Write in notebook.
SWBAT write a polynomial function given the real & complex zeros.
Find a 2nd degree polynomial that has the given zeros of: .{9 , 9 }i i
Assignment:Write a polynomial function with real coefficients that has
the given zeros:
1.{9 , 9 } degree of 2
2. 0,2,3 0 has multiplicity of 3, degree of 5
3. 4,3 ,3 degree of 3
4. 3, 3 degree of 2
5. 2, 4 2 has multiplicity of 2, degree of 4
i i
i i
i