2.2 Polynomial Functions of Higher Degree

2.2: Polynomial Functions of Higher Degree

Sketching Polynomial Graphs

• Polynomial graphs are continuous with smooth and round curves. 

• There are ways to determine what a graph will look like without graphing 

Determining End Behaviors

Leading Coefficient Test 

• Given the graph of a polynomial function 

• When n is odd:

If the leading coefficient is negative, the graph
rises to the left and falls to the right

Example equation: 

*note that the leading coefficient (-2) is negative and n (3) is odd*

If the leading coefficient is positive, the graph
falls to the left and rises to the right



Example equation: 

*note that the leading coefficient (2) is positive and n (3) is odd*

• When n is even:

If the leading coefficient is negative, the graph
falls to the left and right

Example equation: 
*note that the leading coefficient (-2) is negative and n (2) is even*

If the leading coefficient is positive, the graph
rises to the right and left

Example equation: 
*note that the leading coefficient (2) is positive and n (2) is even*

To help with graphing...Zeros of Polynomial Functions

• Given the polynomial function f of degree n

• The function has AT MOST n zeros
• Simply factor to find the zeros!

• The function has AT MOST n extrema (relative maximums/minimums)
• Simply graph to find the extrema!