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How does the highest power of x classify a polynomial function?

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A graph of the function f(x) = x cubed minus 3x plus 2 is shown on a blue background, with a red curve passing through key points. Local maximum and minimum points are marked with black dots at x equals negative 1 and x equals 1, illustrating important features of the curve. — function Plot of the cubic equation f(x) = x³ − 3x + 2. The plotted points are where changes in curvature occur.

In mathematics, a polynomial function is classified by its degree, which is defined as the highest power of the independent variable appearing in the expression.123

When a polynomial involves a single unknown, this degree determines its specific classification. Special names are commonly assigned to these functions based on the highest power of the variable:

Linear: The highest power is 1.3
Quadratic: The highest power is 2.3
Cubic: The highest power is 3.3
Quartic: The highest power is 4.3
Quintic: The highest power is 5.3

By identifying the highest exponent, mathematicians can categorize the function and better understand its behavior, such as its shape when plotted in analytic geometry.3