Polynomial Degree and End Behavior

Identify the sign of the leading coefficient and the degree of the polynomial.

• Leading Coefficient Positive

  Degree - Even

• Leading Coefficient Positive

  Degree - Odd

• Leading Coefficient Negative

  Degree - Even

• Leading Coefficient Negative

  Degree - Odd

• Rises to the right, falls to the left

• Falls to the right, rises to the left

• Rises to the right, rises to the left

• Falls to the right, falls to the left

• Rises to the right, falls to the left

• Falls to the right, rises to the left

• Rises to the right, rises to the left

• Falls to the right, falls to the left

• Rises to the right, falls to the left

• Falls to the right, rises to the left

• Rises to the right, rises to the left

• Falls to the right, falls to the left

• Rises to the right, falls to the left

• Falls to the right, rises to the left

• Rises to the right, rises to the left

• Falls to the right, falls to the left

• Rises to the right, falls to the left

• Falls to the right, rises to the left

• Rises to the right, rises to the left

• Falls to the right, falls to the left

• Rises to the right, falls to the left

• Falls to the right, rises to the left

• Rises to the right, rises to the left

• Falls to the right, falls to the left

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