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5.2 – Evaluate and Graph Polynomial Functions

Name ______________________________________________

(

)

n −1

f (x) = a

+ a

+ ... + a

x + a

n

To write a polynomial in standard form

, we rewrite the

x

x

n −1

n

1

0

polynomial so the variable's exponent to the highest power comes first and then continues to

decrease from left to write. This is also called descending order. Recall that the degree of a

polynomial is the power of the term of the polynomial where the variable is raised to the greatest

power.

1. Put the polynomial in standard form. Then give the degree of the polynomial.

− 8xy

+ 2x

y + 5x

− 3xy

2

2

3

4

3

3

−

− +

2

3

x

y

y

(a)

(b)

3

x x

9 7

x

Note: With 2 variables, use the sum of the powers in

each term.

Degree =

Degree =

The following chart gives the appropriate mathematical term for polynomials of various degree.

Example

Degree of the Polynomial

Type of Polynomial

( )

= −14

0

Constant

f x

( )

= 5x − 7

1

Linear

f x

( )

2

Quadratic

= 4x

+ x − 9

2

f x

( )

3

Cubic

= x

− x

+ 3x − 1

3

2

f x

( )

4

Quartic

= x

+ 2x

− 1

4

2

f x

In mathematics, when you are asked to evaluate, you should expect an answer that is a number

(as opposed to an expression). You already know how to evaluate a function by direct

substitution, but we are going to learn a second option for this procedure.

2. Evaluate the function by direct substitution

( )

= 2x

− 5x

− 4x + 8

4

3

a)

when x = 3

(

f x

( )

= −x

− x

− x − 1

x = −1

3

2

(b)

when

f x

Suggestion: To be extra sure about your signs, use parentheses each time x appears, and substitute

the value inside each of the ( ).

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