graphing polynomials

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero. They are also known as the roots of the polynomial.

Front

How do you identify the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression. It determines the polynomial's end behavior.

Front

What does it mean for a polynomial to be increasing over an interval?

Back

A polynomial is increasing over an interval if, as x values increase, the corresponding y values also increase.

Front

What are the roots of the function f(x) = x^3 + 4x^2 + 3x?

Back

The roots are x = -3, x = -1, and x = 0.

Front

What is a leading coefficient in 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 a polynomial being odd or even?

Back

An odd-degree polynomial has at least one real root and its ends go in opposite directions. An even-degree polynomial has roots that can be real or complex and its ends go in the same direction.

Front

How do you determine if a polynomial is decreasing over an interval?

Back

A polynomial is decreasing over an interval if, as x values increase, the corresponding y values decrease.

Front

What is the relationship between the degree of a polynomial and the number of roots?

Back

A polynomial of degree n can have up to n roots, counting multiplicities.

Front

What does it mean for a polynomial to have a negative leading coefficient?

Back

A polynomial with a negative leading coefficient will have its ends going downwards, meaning as x approaches positive or negative infinity, the polynomial approaches negative infinity.

Front

How can you find the roots of a polynomial function?

Back

Roots can be found by factoring the polynomial, using the quadratic formula, or applying numerical methods.