algebra 2 5.1 class notes
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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