4-2 Graphing Polynomials

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 2x^3 - 4x^2 + 3x - 5 is a polynomial.

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What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 3x^4 + 2x^3 - x + 7, the degree is 4.

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What is a relative maximum?

Back

A relative maximum is a point on the graph of a function where the function value is higher than the values of the function at nearby points. For example, if f(x) has a relative maximum at x = a, then f(a) > f(x) for all x near a.

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What is a relative minimum?

Back

A relative minimum is a point on the graph of a function where the function value is lower than the values of the function at nearby points. For example, if f(x) has a relative minimum at x = b, then f(b) < f(x) for all x near b.

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What is end behavior of a polynomial?

Back

End behavior describes how the values of a polynomial function behave as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

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How do you determine the end behavior of a polynomial?

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To determine the end behavior of a polynomial, look at the leading term. If the leading coefficient is positive and the degree is even, both ends of the graph will rise. If the leading coefficient is negative and the degree is even, both ends will fall.

Front

What is the leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the end behavior of the polynomial.

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What is the difference between absolute maximum and relative maximum?

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An absolute maximum is the highest point over the entire domain of the function, while a relative maximum is the highest point in a specific interval.

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What does it mean for a polynomial to be continuous?

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A polynomial is continuous if there are no breaks, holes, or jumps in its graph. Polynomials are continuous everywhere on their domain.

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What is a turning point in a polynomial graph?

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A turning point is a point where the graph changes direction from increasing to decreasing or vice versa. It corresponds to relative maxima and minima.