Graphs of Polynomials

Front

What is the y-intercept of a polynomial function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, f(0)).

Front

What does the degree of a polynomial indicate?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial, which affects the shape and end behavior of its graph.

Front

What is the end behavior of a polynomial function with an even degree and a positive leading coefficient?

Back

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches +∞.

Front

How do you determine the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial.

Front

What is the difference between odd and even degree polynomials?

Back

Odd degree polynomials have opposite end behaviors (one end goes to +∞ and the other to -∞), while even degree polynomials have the same end behavior (both ends go to +∞ or both to -∞).

Front

What is a root of a polynomial function?

Back

A root (or zero) of a polynomial function is a value of x for which the polynomial equals zero.

Front

How can you find the roots of a polynomial function?

Back

You can find the roots by factoring the polynomial, using the quadratic formula, or applying numerical methods.

Front

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

Back

The leading term determines the end behavior and the growth rate of the polynomial as x approaches ±∞.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is expressed as a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

Front

What does it mean for a polynomial to be factored completely?

Back

A polynomial is factored completely when it is expressed as a product of irreducible polynomials over the given number system.