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 the end behavior of a polynomial describe?

Back

The end behavior of a polynomial describes how the values of the polynomial behave as the input (x) approaches positive or negative infinity.

Front

What is a root of a polynomial?

Back

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

Front

What is multiplicity in relation to polynomial roots?

Back

Multiplicity refers to the number of times a particular root appears in a polynomial. A root with multiplicity greater than 1 indicates that the root is repeated.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior can be determined by the leading term of the polynomial. If the leading coefficient is positive and the degree is even, both ends rise; if negative, both ends fall. If the degree is odd, one end rises and the other falls.

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

What is the significance of the y-intercept in a polynomial graph?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the value of the polynomial when x=0.

Front

How can you identify the number of roots a polynomial has?

Back

The number of roots of a polynomial can be determined by its degree. A polynomial of degree n can have up to n roots.

Front

What is the difference between even and odd degree polynomials in terms of their graphs?

Back

Even degree polynomials have graphs that are symmetric about the y-axis, while odd degree polynomials have graphs that are symmetric about the origin.