algebra 2 5.1 class notes

Polynomial FunctionsSection 5.1

The degree of a polynomial is the greatest exponent of the variable.

The degree of a polynomial is the greatest exponent of the variable.

The degree of a polynomial is the greatest exponent of the variable.

1

The degree of a polynomial is the greatest exponent of the variable.

1

Degree Name of polynomial

0 Constant

1 Linear

2 Quadratic

3 Cubic

4 Quartic

5 Quintic

The degree of a polynomial is the greatest exponent of the variable.

1 quadratic

Degree Name of polynomial

0 Constant

1 Linear

2 Quadratic

3 Cubic

4 Quartic

5 Quintic

1

Signs in front of terms go with the

term.

1

Signs in front of terms go with the

term.

1

Signs in front of terms go with the

term.

1

Signs in front of terms go with the

term.

1

Signs in front of terms go with the

term.

1

Signs in front of terms go with the

term.

1

Write each polynomial in standard form. Then classify it by degree and state the leading coefficient.

1. 4x3 3 + 2x2

4. 8 x5 + 9x2 2x

3. 6x + 2x4 2 2. 3 + 24x2

5. -13 + x 6. 8

Write each polynomial in standard form. Then classify it by degree and state the leading coefficient.

1. 4x3 3 + 2x2

4. 8 x5 + 9x2 2x

3. 6x + 2x4 2 2. 3 + 24x2

5. -13 + x 6. 8

4x3 + 2x2 3CubicL.C. 4

Write each polynomial in standard form. Then classify it by degree and state the leading coefficient.

1. 4x3 3 + 2x2

4. 8 x5 + 9x2 2x

3. 6x + 2x4 2 2. 3 + 24x2

5. -13 + x 6. 8

4x3 + 2x2 3CubicL.C. 4

24x2 + 3QuadraticL.C. 24

2x4 + 6x 2QuarticL.C. 2

x5 + 9x2 2x + 8 QuinticL.C. -1

x – 13LinearL.C. 1

8ConstantL.C. None

Graph each function using the domain x = -2, -1, 0, 1, 2, 3.

x y

-2

-1

0

1

2

3

Graph each function using the domain x = -2, -1, 0, 1, 2, 3.

x y

-2 -2

-1 2

0 0

1 -2

2 2

3 18

Graph each function using the domain x = -2, -1, 0, 1, 2, 3.

x y

-2 -2

-1 2

0 0

1 -2

2 2

3 18

Graph each function using the domain x = -2, -1, 0, 1, 2, 3.

x y

-2 -2

-1 2

0 0

1 -2

2 2

3 18

Graph each function using the domain x = -2, -1, 0, 1, 2, 3.

x y

-2

-1

0

1

2

3

Graph each function using the domain x = -2, -1, 0, 1, 2, 3.

x y

-2 30

-1 -1

0 0

1 3

2 2

3 15

Graph each function using the domain x = -2, -1, 0, 1, 2, 3.

x y

-2 30

-1 -1

0 0

1 3

2 2

3 15

Graph each function using the domain x = -2, -1, 0, 1, 2, 3.

x y

-2 30

-1 -1

0 0

1 3

2 2

3 15

End behavior of a polynomial function can be found by looking at the leading coefficient and the degree.

Down, Up Up, Down

End behavior of a polynomial function can be found by looking at the leading coefficient and the degree.

Up, Up Down, Down

Predict the end behavior of each polynomial function.

423 3 xxy

xxy 3xxxy 234 34

2710 6 xxy1. 2.

3. 4.

ex. 1264 310 xxxy

Predict the end behavior of each polynomial function.

423 3 xxy

xxy 3xxxy 234 34

2710 6 xxy1. 2.

3. 4.

ex. 1264 310 xxxyDegree is even so ends go in same direction.

Leading coefficient is negative so the right is down.End behavior is Down, Down

Predict the end behavior of each polynomial function.

423 3 xxy

xxy 3xxxy 234 34

2710 6 xxy1. 2.

3. 4.

ex. 1264 310 xxxyDegree is even so ends go in same direction.

Leading coefficient is negative so the right is down.End behavior is Down, Down

Down, Up Down, Down

Up, Down Up, Up

Predict the end behavior of each polynomial function.

423 3 xxy

xxy 3xxxy 234 34

2710 6 xxy1. 2.

3. 4.

ex. 1264 310 xxxyDegree is even so ends go in same direction.

Leading coefficient is negative so the right is down.End behavior is Down, Down

Down, Up Down, Down

Up, Down Up, Up