Unit 4 Lesson 3: Examining Zeros

Unit 4 Lesson 3
Examining Zeros

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Make sure you have all of the information copied down correctly!

​

Complete the table from Friday!

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CONJECTURE (Fill this out on your notes page!)

If the multiplicity of a zero is EVEN, then the graph will ​

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at that zero.

If the multiplicity of a zero is ODD, then the graph will ​

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at that zero.

​PART 2

In lesson one of the polynomials unit, we were given zeros and a point on the graph of a polynomial and asked to find the equation.
Today we will add complex zeros.

-Imaginary roots are NOT visible on the graph
-If (a+bi) is a root of the polynomial then (a-bi) must ALSO be a root and vice versa

Drag and Drop

If (6 + 5i) is a root, then

Placeholder

must also be a root



If - 8i is a root, then​

Placeholder

must also be a root



If (2 - 7i) is a root, then​

Placeholder

must also be a root

Drag these tiles and drop them in the correct blank above

(6 - 5i)

(6 + 5i)

8i

-8i

(2 + 7i)

(2 - 7i)

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Math Response

1. A polynomial has the roots 2, 3 multiplicity of 2, and 4i. The y-intercept is 15.

a) What root is not listed?

Type answer here

Correct Answer: -4i

Deg^°

Rad

1A

Math Response

1. A polynomial has the roots 2, 3 multiplicity of 2, and 4i. The y-intercept is 15.

b) Find the equation of the polynomial in factored form. (Type your answer as y = )

Type answer here

Correct Answer: y=\frac{-5}{96}\left(x-2\right)\left(x-3\right)^2\left(x-4i\right)\left(x+4i\right)

Deg^°

Rad

1B
1C

Dropdown

A polynomial has the roots 2, 3 multiplicity of 2, and 4i. The y-intercept is 15.



d) Describe the end behavior and the possible number of turning points:



$$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow$$ ​

Select answer

$$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow$$ ​ ​

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Maximum number of turning points = ​

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1D

The degree will be five for two reasons:

1) We have 5 x-intercepts
(2, 0) multiplicity of 1 (4i) multiplicity of 1
(3, 0) multiplicity of 2 (-4i) multiplicity of 1
We add the multiplicities to get the degree (1 + 2 + 1 + 1 = 5)

​2) If you convert your equation to standard form your degree will be 5

Math Response

2. A polynomial has the roots 2, and 1i. The y-intercept is -1.

a) What root is not listed?

Type answer here

Correct Answer: -1i

Deg^°

Rad

2A

Math Response

2. A polynomial has the roots 2, and 1i. The y-intercept is -1.

b) Find the equation of the polynomial (Type your answer as y = )

Type answer here

Correct Answer: y=\frac{1}{2}\left(x-2\right)\left(x-1i\right)\left(x+1i\right)

Deg^°

Rad

2B
2C

Dropdown

A polynomial has the roots 2, and 1i.

The y-intercept is -1.

d) Describe the end behavior and the possible number of turning points:



$$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow$$ ​
Select answer


$$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow$$ ​ ​
Select answer


Maximum number of turning points = ​
Select answer

2D

Once you finish this page and answer the Wayground questions that go along with it, you are done for today.
If you want extra practice, there is Unit 4 homework that is posted. Tomorrow will be a day of practice on what we have learned in Unit 4 so far :)

​If you are not working on the homework, you need to find something to work on silently.