Algebra II Section 5.1 Day 1
Polynomial Functions
Name: _____________________
Learning Goals:
 I can write a polynomial in standard form and classify it.
 I can determine the end behavior of a polynomial based on the degree.
Remember how the differences can tell us if data is linear or quadratic??
What about the following data?
Is the data linear?
Is the data quadratic?
What kind of polynomial do you think the data represents?
Today we are going to explore polynomials with degrees higher than 2!
Vocabulary:
Monomial: is a real number, a variable, or a product of a real number and one or more variables with whole
number exponents. Example:
Degree of a monomial: in one variable is the exponent of the variable. Example:
Polynomial: is a monomial or sum of monomials. Examples:
Degree of a polynomial: in one variable is the greatest degree among its monomial terms. Examples:
Standard form of a polynomial: arrange the terms by degree in descending order
P( x)  an xn  an1 x n1   _ a1 x  a0 Example:
Match each word in Column A with the matching polynomial in Column B.
Column A
Column B
1. cubic
A. 8
2. linear
B. 3x4 + 5x2  1
3. quartic
C. 2x2  2
4. quintic
D. 7x3 + 3x2 + 4
5. constant
E. x + 10
6. quadratic
F. 6x5 + 3x3 + 11x + 3
Match each polynomial in Column A with the matching word in Column B.
Column A
Column B
7. 5x3 + 7x
A. trinomial(3 terms)
8. 4x5 + 6x2 + 3
B. monomial(1 term)
9. 8x4
C. binomial(2 terms)
Write each polynomial in standard form then use the words from the lists below to name each polynomial
by its degree and its number of terms.
Linear( )
Monomial( )
quadratic( )
Number of Terms
binomial( )
10. 3 2x + 4x2 __________________________
11. 6x3 ___________________________
12. 7x3  4 + 3x5 _________________________
13. 3 – 8x ___________________________
14. 2x4 + 5x2 __________________________
Degree
cubic( )
trinomial( )
quartic( )
quintic( )
The degree of a polynomial function affects the shape of its graph and determines the maximum number of
TURNING POINTS or places where the graph changes direction. It affects the END BEHAVIOR or the directions of
the graph to the far left and to the far right. A function is INCREASING when the y-values increase as x-values
increase. A function is DECREASING when the y-values decrease as x-values increase.
Examples:
Coefficient=a
Exponent=n
To describe the end behavior of a polynomial function, you only look at the leading term!
Consider the leading term of 𝑦 = −4𝑥 3 + 2𝑥 2 + 7. What is the end behavior of the graph?
a) The coefficient of the leading term is positive/negative (circle one).
b) The exponent of the leading term is even/odd (circle one).
c) Circle the graph that illustrates the correct end behavior.
Determine the end behavior of the graph of each polynomial function.
1. y = 3x4 + 6x3  x2 + 12
2. y = 50  3x3 + 5x2
3. y = x + x2 + 2
4. y = 4x2 + 9  5x4  x3
5. y = 12x4  x + 3x7  1
6. y = 2x5 + x2  4