Chapter

Objective
Students
will be able to…

Standard(s)

Help/Examples

Practice

8.1.1

Describe the graph of a
polynomial given its equation in factored form

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Polynomial end behavior
Polynomial end behavior example


8.1.2

Consolidate, generalize
the graph of a polynomial given its equation in factored form

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Determine the xintercepts of a polynomial function by analyzing its factors
Determine the end behavior of a graph by analyzing its equation
Determine when a polynomial function changes sign
Sketch the graph of a higher degree polynomial
Determine the equation of a polynomial by analyzing its graph 

8.1.3

Write exact equations for
the graphs of polynomial functions given the x‑intercepts
and one additional point

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Writing Polynomial Equations given the Zeros of the Functions


8.2.1

Solve equations using
imaginary and complex numbers

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Introduction to i and imaginary numbers
Imaginary roots of negative numbers
Introduction to complex numbers

https://www.khanacademy.org/math/algebra2/complexnumbersa2/complex_numbers/e/theimaginaryunitandcomplexnumbers

8.2.2

Write the equations for
quadratic functions given the roots

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NCN.8 (+)
NCN.9 (+)

Write a Polynomial Function with Complex Zeros


8.2.2

Practice operations with
complex numbers

NCN.2

Calculating i raised to arbitrary exponents
Adding complex numbers
Subtracting complex numbers
Multiplying complex numbers
Dividing complex numbers

Imaginary unit powers
Adding and subtracting complex numbers
Multiplying complex numbers
Dividing complex numbers

8.2.3

Use the complex plane as a
way to visualize complex numbers and complex roots for quadratic functions

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NCN.7
NCN.9 (+)

Plotting complex numbers on the complex plane


8.2.3

Calculate the absolute
value of a complex number

NCN.2

Absolute value of a complex number

Absolute value of complex numbers

8.3.1

use polynomial division to
find factors of polynomials

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Polynomial division
Dividing polynomials 1
Dividing polynomials with remainders
Synthetic division
Synthetic division example 2


8.3.2

Use the Integral Zero
Theorem, polynomial division and the Factor Theorem to find integral roots
and to find all roots of polynomials with degree greater than two

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NCN.8 (+)
NCN.9 (+)

Example: Factoring a fourth degree expression
Factoring 5th degree polynomial to find real zeros
Identifying graph based on roots

Using zeros to graph polynomials

8.3.3

Use knowledge of
polynomial functions and graphs to maximize volume of a tank

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NCN.9 (+)


