5.28 End Behavior Patterns

The degree of a polynomial can be determined by the largest powered monomial of the polynomial.  
What is the degree of the polynomial:
f(x) = 3x² + 4x - 5

• Degree 2  (quadratic)
• Degree 3 (cubic)
• Degree 4 (quartic)
• Degree 5 (quintic)

The leading coefficient is the coefficient of the largest degree monomial for the polynomial.
What is the leading coefficient for the polynomial f(x) = 2x³ + 4x - 5

• The leading coefficient is 2
• The leading coefficient is 3
• The leading coefficient is 4
• The leading coefficient is 5

The leading coefficient is the coefficient of the largest degree monomial for the polynomial.
Is the leading coefficient for the polynomial positive or negative?

f(x) = -3x² - 5x - 4

• negative

• positive

How many stars are on the American Flag?

• 13

• 50

• 51

• 62

The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph.  
Enter the polynomial function into a graphing calculator or online graphing tool to determine the end behavior.
f(x) = 2x³ - x + 5

Match the graph with the correct information regarding the leading term.

• Positive leading coefficient, even degree

• Positive leading coefficient, odd degree

• Negative leading coefficient, even degree

• Negative leading coefficient, odd degree

Match the graph with the correct information regarding the leading term.

• Positive leading coefficient, even degree

• Positive leading coefficient, odd degree

• Negative leading coefficient, even degree

• Negative leading coefficient, odd degree

What was the last movie Walt Disney was able to work on before he died?

• Cinderella

• The Jungle Book

• Mary Poppins

• 101 Dalmatians

Match the graph with the correct information regarding the leading term.

• Positive leading coefficient, even degree

• Positive leading coefficient, odd degree

• Negative leading coefficient, even degree

• Negative leading coefficient, odd degree

Match the graph with the correct information regarding the leading term.

• Positive leading coefficient, even degree

• Positive leading coefficient, odd degree

• Negative leading coefficient, even degree

• Negative leading coefficient, odd degree