Polynomial Graphing

What is the relative minimum?

• (5, -4)

• (3, 0)

What are the roots of the quadratic function?

• -4 and -2

• 4 and 2

• -4 and 2

• 4 and -2

How many roots does the polynomial have?

• 4

• 3

• 2

• 1

What are the roots of the polynomial?

• -3, 0, and 3

• 0

• -2, 10, and -10

• 11, 0 and -11

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

• 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) = -x⁵ - 4x +2

• Left up  Right up

• Left up  Right down

• Left down  Right up

• Left down  Right down

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even

• Leading Coefficient Positive
  Degree - Odd

• Leading Coefficient Negative
  Degree - Even

• Leading Coefficient Negative
  Degree - Odd

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even

• Leading Coefficient Positive
  Degree - Odd

• Leading Coefficient Negative
  Degree - Even

• Leading Coefficient Negative
  Degree - Odd