Algebra 2 Polynomial Functions 3.1, 3.5

Front

What is the leading term of a polynomial and how does it affect end behavior?

Back

The leading term of a polynomial is the term with the highest degree. It determines the end behavior of the polynomial function. If the leading coefficient is positive and the degree is even, the ends of the graph rise. If the leading coefficient is negative and the degree is even, the ends fall. If the degree is odd, one end rises and the other falls.

Front

Define the leading-term test in relation to polynomial functions.

Back

The leading-term test is a method used to determine the end behavior of a polynomial function based on its leading term. It helps to predict how the graph behaves as x approaches positive or negative infinity.

Front

What is the degree of a polynomial and how is it determined?

Back

Front

How do you find the number of possible zeros of a polynomial?

Back

The number of possible zeros of a polynomial is equal to its degree. For example, a polynomial of degree 3 can have up to 3 real zeros.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the leading term. It affects the direction of the graph's end behavior. A positive leading coefficient means the graph rises to the right, while a negative leading coefficient means it falls to the right.

Front

Explain the relationship between the degree of a polynomial and the number of turns in its graph.

Back

The maximum number of turns in the graph of a polynomial is one less than its degree. For example, a polynomial of degree 4 can have up to 3 turns.

Front

What are imaginary solutions in the context of polynomial equations?

Back

Imaginary solutions occur when a polynomial has no real roots. They are represented as complex numbers and arise from the square roots of negative numbers.

Front

How do you determine the number of imaginary solutions in a polynomial?

Back

To determine the number of imaginary solutions, factor the polynomial and count the number of times the factors yield negative values under the square root. Each pair of complex conjugate solutions corresponds to two imaginary solutions.

Front

What is the difference between even and odd degree polynomials in terms of their end behavior?

Back

Even degree polynomials have the same end behavior on both sides (both rise or both fall), while odd degree polynomials have opposite end behavior (one side rises and the other falls).

Front

Provide an example of a polynomial function and identify its degree, leading coefficient, and possible zeros.

Back