5-Minute Check Lesson 4-1

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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

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

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

Degree of a polynomial -

• Roots or zeros of a polynomial -
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

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