Polynomial End Behavior Review

Front

What is the end behavior of a polynomial function with a leading coefficient that is negative and an odd degree?

Back

The end behavior will be down on the left and up on the right.

Front

What is the end behavior of a polynomial function with a leading coefficient that is positive and an even degree?

Back

The end behavior will be up on both ends.

Front

Define the degree of a polynomial.

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is a leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How does the degree of a polynomial affect its end behavior?

Back

Odd degree polynomials have opposite end behaviors, while even degree polynomials have the same end behavior.

Front

What does it mean for a polynomial to 'pass through' the x-axis?

Back

It means that the polynomial has a root at that x-value, and the graph intersects the x-axis.

Front

What does it mean for a polynomial to 'touch and turn around' at a point on the x-axis?

Back

It means that the polynomial has a repeated root at that x-value, and the graph touches the x-axis but does not cross it.

Front

Identify the degree and leading coefficient of the polynomial: y = 3x^4 - 2x^2 + 5.

Back

Degree: 4, Leading Coefficient: 3.

Front

Identify the degree and leading coefficient of the polynomial: y = -x^3 + 4x + 1.

Back

Degree: 3, Leading Coefficient: -1.

Front

What is the end behavior of the polynomial y = 2x^2 - 3?

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.