Graphing Polynomials

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

Front

What does it mean for a polynomial to have zeros?

Back

Zeros of a polynomial are the values of x for which the polynomial evaluates to zero. They represent the x-intercepts of the graph.

Front

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

Back

The y-intercept of a polynomial function can be found by evaluating the function at x=0.

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 is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the direction of the graph's end behavior and affects the shape of the graph.

Front

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

Back

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

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses the polynomial as a product of its linear factors.

Front

How do you identify the zeros from a factored polynomial?

Back

To identify the zeros from a factored polynomial, set each factor equal to zero and solve for x.

Front

What is the relationship between the degree of a polynomial and its graph?

Back

The degree of a polynomial affects the number of turns in its graph and the end behavior.