Polynomial Graphs

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or 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.

Front

What does it mean for a root to have a multiplicity of 2?

Back

A root with a multiplicity of 2 means that the root is repeated twice, and the graph will 'bounce' off the x-axis at that point.

Front

How does the leading coefficient affect the graph of a polynomial?

Back

The leading coefficient determines the direction of the graph's ends: if positive, the graph rises to the right; if negative, it falls to the right.

Front

What is an absolute minimum point on a polynomial graph?

Back

An absolute minimum point is the lowest point on the graph of the polynomial, where the function value is less than or equal to all other values.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which the polynomial evaluates to zero.

Front

What happens to the graph at a zero with odd multiplicity?

Back

At a zero with odd multiplicity, the graph will cross the x-axis.

Front

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

Back

The leading term, which is the term with the highest degree, determines the end behavior of the polynomial graph.

Front

How can you determine the number of zeros a polynomial has?

Back

The number of zeros of a polynomial is at most equal to its degree, according to the Fundamental Theorem of Algebra.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a function that consists of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.