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5-Minute Check Lesson 4-1

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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?

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 -

- 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 ______

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.

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