Polynomial Degree and End Behavior

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

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) = -4x³ + 5x - 2

• 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) = -4x³ - 2x + 5

• The leading coefficient is -2

• The leading coefficient is 3

• The leading coefficient is -4

• The leading coefficient is 5

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

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

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

• 2

• 3

• 4

• 1

• Rises on the left and right

• Rises on left, falls on right

• Falls on the left, rises on the right

• Falls on the left and right

• Rises on the left and right

• Rises on left, falls on right

• Falls on the left, rises on the right

• Falls on the left and right

Tags

CCSS.HSF-IF.C.7A