Review: Polynomial Sketching

Front

What is a polynomial?

Back

Front

What is the degree of a polynomial?

Back

Front

What does it mean for a polynomial to have a 'snake' at an x-intercept?

Back

A polynomial has a 'snake' at an x-intercept if the factor corresponding to that intercept has an odd multiplicity, causing the graph to touch the x-axis and turn around.

Front

How do you determine the end behavior of a polynomial?

Back

The end behavior of a polynomial is determined by its leading term. If the leading coefficient is positive, the ends of the graph will rise in the same direction; if negative, they will fall in opposite directions.

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. It influences the end behavior of the graph.

Front

What is the significance of the x-intercepts of a polynomial?

Back

The x-intercepts of a polynomial are the values of x for which the polynomial equals zero. They indicate where the graph crosses or touches the x-axis.

Front

What is a factor of a polynomial?

Back

Front

What is the relationship between the degree of a polynomial and the number of x-intercepts?

Back

The maximum number of x-intercepts of a polynomial is equal to its degree. However, some x-intercepts may be repeated (multiplicity) or complex.

Front

What is multiplicity in the context of polynomial roots?

Back

Multiplicity refers to the number of times a particular root (or x-intercept) appears in a polynomial. A root with odd multiplicity will cross the x-axis, while one with even multiplicity will touch the x-axis.

Front

How do you find the y-intercept of a polynomial?

Back