Algebra 2 Ch 2.2 Evaluate and Graph Polynomials Functions for PDF
Algebra 2 Ch 2.2 Evaluate and Graph Polynomials Functions for PDF.notebook October 12, 2012
Evaluate and Graph Polynomial Functions 2.2 Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions A polynomial function is in the form of:
• Standard form of Polynomials • Direct Substitution • Synthetic Substitution • End Behavior
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions
The degree of a function is the highest exponent in the polynomial.
The degree of the polynomial above is 4.
Oct 87:38 PM
Type
0
Constant
1
Linear
2
Quadratic
3
Cubic
4
Quartic
Standard Form
The leading coefficient of the polynomial above is 3.
Oct 87:38 PM
Evaluate and Graph Polynomial Functions Degree
Evaluate and Graph Polynomial Functions The leading coefficient of a function is the number in front of variable that determines the degree of the function..
Example
Evaluate and Graph Polynomial Functions Polynomial or not a polynomial?
NO
YES
YES NO
Oct 87:38 PM
Oct 87:38 PM
1
Algebra 2 Ch 2.2 Evaluate and Graph Polynomials Functions for PDF.notebook October 12, 2012
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions
How to evaluate a function.
In this case, everywhere you see an x, you replace it with a two.
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions
There is a different way to evaluate a functions and that is with synthetic substitution.
Evaluate To set up synthetic substitution, start with a table.
We will evaluate the same function using this new technique.
xvalue
2
3
4
1
10
7 coefficients
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions
Synthetic Substitution
Synthetic Substitution
2
3
4
1
10
7
2
3
6 3
2
Oct 87:38 PM
3
4
1
6
4
2
3
10
7
Oct 87:38 PM
2
Algebra 2 Ch 2.2 Evaluate and Graph Polynomials Functions for PDF.notebook October 12, 2012
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions Synthetic Substitution
Synthetic Substitution 2
2
3
4
1
10
6
4
6
2
3
16
3
7
3
3
Oct 87:38 PM
Evaluate and Graph Polynomial Functions End behavior: What is happening to the graph of the function as x approaches positive infinity and negative infinity.
4
1
10
7
6
4
6 32
2
3
16 39
Oct 87:38 PM
Evaluate and Graph Polynomial Functions Degree: odd Leading Coefficient: positive
We will look at the degree of the function and whether the leading coefficient is positive or negative.
Oct 87:38 PM
Evaluate and Graph Polynomial Functions Degree: odd Leading Coefficient: negative
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions Degree: even Leading Coefficient: positive
Oct 87:38 PM
3
Algebra 2 Ch 2.2 Evaluate and Graph Polynomials Functions for PDF.notebook October 12, 2012
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions
Degree: even Leading Coefficient: negative
To graph a function, a table of values is useful.
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions
x
3
2
1
0
1
2
3
y
81
35
15
9
5
9
45
x
3
2
1
0
1
2
3
y
81
35
15
9
5
9
45
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions
x
3
2
1
0
1
2
3
y
76
12
2
4
0
4
22
Oct 87:38 PM
Evaluate and Graph Polynomial Functions x
3
2
1
0
1
2
3
y
76
12
2
4
0
4
22
Oct 87:38 PM
4
Algebra 2 Ch 2.2 Evaluate and Graph Polynomials Functions for PDF.notebook October 12, 2012
Evaluate and Graph Polynomial Functions 2.2 Evaluate and Graph Polynomial Functions • Standard form of Polynomials • Direct Substitution • Synthetic Substitution • End Behavior
Oct 87:38 PM
5
Evaluate and Graph Polynomial Functions 2.2 Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions A polynomial function is in the form of:
• Standard form of Polynomials • Direct Substitution • Synthetic Substitution • End Behavior
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions
The degree of a function is the highest exponent in the polynomial.
The degree of the polynomial above is 4.
Oct 87:38 PM
Type
0
Constant
1
Linear
2
Quadratic
3
Cubic
4
Quartic
Standard Form
The leading coefficient of the polynomial above is 3.
Oct 87:38 PM
Evaluate and Graph Polynomial Functions Degree
Evaluate and Graph Polynomial Functions The leading coefficient of a function is the number in front of variable that determines the degree of the function..
Example
Evaluate and Graph Polynomial Functions Polynomial or not a polynomial?
NO
YES
YES NO
Oct 87:38 PM
Oct 87:38 PM
1
Algebra 2 Ch 2.2 Evaluate and Graph Polynomials Functions for PDF.notebook October 12, 2012
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions
How to evaluate a function.
In this case, everywhere you see an x, you replace it with a two.
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions
There is a different way to evaluate a functions and that is with synthetic substitution.
Evaluate To set up synthetic substitution, start with a table.
We will evaluate the same function using this new technique.
xvalue
2
3
4
1
10
7 coefficients
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions
Synthetic Substitution
Synthetic Substitution
2
3
4
1
10
7
2
3
6 3
2
Oct 87:38 PM
3
4
1
6
4
2
3
10
7
Oct 87:38 PM
2
Algebra 2 Ch 2.2 Evaluate and Graph Polynomials Functions for PDF.notebook October 12, 2012
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions Synthetic Substitution
Synthetic Substitution 2
2
3
4
1
10
6
4
6
2
3
16
3
7
3
3
Oct 87:38 PM
Evaluate and Graph Polynomial Functions End behavior: What is happening to the graph of the function as x approaches positive infinity and negative infinity.
4
1
10
7
6
4
6 32
2
3
16 39
Oct 87:38 PM
Evaluate and Graph Polynomial Functions Degree: odd Leading Coefficient: positive
We will look at the degree of the function and whether the leading coefficient is positive or negative.
Oct 87:38 PM
Evaluate and Graph Polynomial Functions Degree: odd Leading Coefficient: negative
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions Degree: even Leading Coefficient: positive
Oct 87:38 PM
3
Algebra 2 Ch 2.2 Evaluate and Graph Polynomials Functions for PDF.notebook October 12, 2012
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions
Degree: even Leading Coefficient: negative
To graph a function, a table of values is useful.
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions
Evaluate and Graph Polynomial Functions
x
3
2
1
0
1
2
3
y
81
35
15
9
5
9
45
x
3
2
1
0
1
2
3
y
81
35
15
9
5
9
45
Oct 87:38 PM
Oct 87:38 PM
Evaluate and Graph Polynomial Functions
x
3
2
1
0
1
2
3
y
76
12
2
4
0
4
22
Oct 87:38 PM
Evaluate and Graph Polynomial Functions x
3
2
1
0
1
2
3
y
76
12
2
4
0
4
22
Oct 87:38 PM
4
Algebra 2 Ch 2.2 Evaluate and Graph Polynomials Functions for PDF.notebook October 12, 2012
Evaluate and Graph Polynomial Functions 2.2 Evaluate and Graph Polynomial Functions • Standard form of Polynomials • Direct Substitution • Synthetic Substitution • End Behavior
Oct 87:38 PM
5
