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Alg 2 BC U6 Day 1 - Intro to Polynomials, End Behavior

Warm-up (on a separate piece of paper):

1. WITHOUT a calculator, graph the following polynomial, showing correct end behavior, accurate

x-intercepts and accurate y-intercept: [pic]

2. WITHOUT using FOIL (or "BIG FOIL"), expand: (2x-y3)7

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Polynomials:

Degree of a TERM: __________________________________________________________

Degree of a POLYNOMIAL: __________________________________________________

Polynomial Classification based on DEGREE:

Degree 0 – Degree 3 -

Degree 1 – Degree 4 -

Degree 2 – Degree 5 –

Degree n

Polynomials Classification based on NUMBER OF TERMS:

One term – Three terms –

Two terms – Four or more terms --

Write each polynomial in standard form. Give the leading coefficient. Then classify by degree and number of terms.

a) y = -7x + 5x4 b) y = x2 – 4x + 3x3 + 2x

c) y = x(2x)(4x + 1) d) y = (x + 1)(x – 1)(x + 2)

Even function: A function is even if _____________________ for all x in domain.

If the point (x,y) is on the graph, then the point ______ is on the graph.

An even function is symmetric with respect to _________________.

Odd function: A function is odd if _____________________ for all x in domain.

If the point (x,y) is on the graph, then the point ______ is on the graph.

An odd function is symmetric with respect to _________________.

Determine whether each function is odd, even or neither by substituting “-x” in for each “x”:

1. f(x) = x2 + 1

2. f(x) = x3 + x

3. f(x) = x3-x2+2

Where do you think the names “odd” and “even” function come from?

End Behavior of Polynomial Functions:

What happens when: x is “very positive” (approaches [pic]) and

x is “very negative” (approaches [pic])?

The end behavior of a graph describes the far left and far right portions of the graph.

up/up down/down up/down down/up

Example: Determine the end behavior of each graph.

a) y = 3x + 2

b) y = 2x3 – 4x4 + 7

c) y = -x3 – x

Modeling data with polynomial functions:

Using a calculator, find a cubic model for the given data:

|X |0 |5 |10 |15 |20 |

|Y |10.1 |2.8 |8.1 |16.0 |17.8 |

1. Enter the date into L1 and L2 using the STAT function on your calculator.

2. Turn on STAT PLOT by going to 2nd Y = and highlighting plot 1.

3. Graph the scatterplot by going to ZOOMSTAT (Zoom 9)

4. Using the STAT function, find the cubic regression (CUBICREG), saving it into Y2.

5. Graph the scatterplot with the cubic regression on the same set of axes.

Equation: _________________________________

Using the equation you found, approximate y when x = 25, 50, and 100. (CALC Value)

Using the equation you found, approximate any “zeros” of the function. (CALC Zero)

Worksheet 1:

Determine if the following functions are even, odd or neither:

1. [pic] 2. [pic]

3. [pic] 4.[pic]

5. [pic] 6. [pic]

Determine the end behavior of the graph of each function:

7. [pic] 8. [pic]

9. [pic] 10. [pic]

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Standard Form for a Polynomial function of Degree n:

[pic]

Where n is a _____________________ and an, an-1, … a0 are _________ ________________.

Note that the terms are written in __________________ ___________________.

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