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5-Minute Check Lesson 4-1. 5-Minute Check Lesson 4-1. 5-Minute Check Lesson 4-1. 5-Minute Check Lesson 4-1. 4 -1 : Polynomial Functions. LESSON ESSENTIAL QUESTIONS How do we determine the roots of polynomial equations? How do they exponents and degree of a function relate to its graph?.

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4 1 polynomial functions

4 -1 : Polynomial Functions

LESSON ESSENTIAL QUESTIONS

  • How do we determine the roots of polynomial equations?

  • How do they exponents and degree of a function relate to its graph?


Families of graphs
Families of Graphs

On multi-block paper, sketch the following “parent” functions which serve as common end behavior models:


On pg 207 in your book
On Pg 207 in your book



Polynomial functions
Polynomial Functions

  • For a quadratic function, what is the maximum number of:

    x-intercepts/zeros _____ turning points _____

  • For a cubic function, what is the maximum number of:

    x-intercepts/zeros ______ turning points ______


Degrees of polynomials
Degrees of Polynomials

For any polynomial function, the following apply:

  • Maximum # turning points = (DEGREE - 1)

  • Maximum # of roots (x-intercepts) = (DEGREE)

    For each polynomial, identify the max. number of roots and turning points and sketch a model:

Now use your graphing calculator to find the roots and turning points.


Homework
Homework

  • Pg 210 # 10-18E, 29-31A, 40-44E, 52-54A


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