Analyze Polynomial Function Behavior

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

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

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Back

Quadratic (degree 2)

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Back

Cubic (degree 3)

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms.

Front

What is the leading coefficient of a polynomial?

Back

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

Front

Describe the end behavior of a polynomial function with an even degree and a positive leading coefficient.

Back

As x approaches positive or negative infinity, the function approaches positive infinity.

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Describe the end behavior of a polynomial function with an odd degree and a negative leading coefficient.

Back

As x approaches positive infinity, the function approaches negative infinity, and as x approaches negative infinity, the function approaches positive infinity.

Front

What is the significance of the leading coefficient in determining end behavior?

Back

The sign of the leading coefficient (positive or negative) and the degree (even or odd) determine the direction in which the graph of the polynomial will rise or fall at the ends.