Polynomial End Behavior

• 3

• -4

• 4

• 2

• 3

• 6

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.
What is the leading coefficient for the polynomial f(x) = -3x² - 5x - 4

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

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

• Left up    Right up
• Left up   Right down
• Left down   Right up
• Left down   Right down

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) = -2x² + 3x 

• Left up    Right up
• Left up   Right down
• Left down  Right up
• Left down   Right down

Determine the end behavior of the polynomial by identifying the degree and leading coefficient.

f(x) = 5x⁴ - x + 6

• UP-UP

• UP-DOWN

• DOWN-UP

• DOWN-DOWN

Is the degree of the graphed polynomial even or odd?

• Even

• Odd

Using the graph, what can we assume about the equation?

• Degree - Even

  Leading Coefficient - Positive

• Degree - Odd

  Leading Coefficient - Positive

• Degree - Even

  Leading Coefficient - Negative

• Degree - Odd

  Leading Coefficient - Negative