Polynomial Graphs

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What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

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What does the degree of a polynomial indicate?

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The degree of a polynomial indicates the highest power of the variable in the polynomial. It determines the polynomial's end behavior and the maximum number of zeros it can have.

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What is the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the direction of the graph as x approaches positive or negative infinity.

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How do you find the zeros of a polynomial?

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To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable. The solutions are the x-values where the graph intersects the x-axis.

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What is the end behavior of a polynomial function?

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The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the degree and leading coefficient.

Front

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

Back

As x approaches positive or negative infinity, the function rises in both directions.

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

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

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

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As x approaches positive or negative infinity, the function falls in both directions.

Front

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

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

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What are the factors of a polynomial?

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Factors of a polynomial are expressions that can be multiplied together to yield the polynomial. For example, in y = (x - 1)(x + 2), (x - 1) and (x + 2) are factors.