Polynomial Graphs

Front

What is the degree of a polynomial function?

Back

The degree of a polynomial function is the highest power of the variable in the polynomial.

Front

How does the leading coefficient affect the graph of a polynomial?

Back

The leading coefficient determines the direction of the graph's ends: if positive, the right end rises; if negative, the right end falls.

Front

What is the general form of a polynomial function?

Back

A polynomial function is generally expressed as f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n is the leading coefficient and n is the degree.

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 equals zero; they represent the x-intercepts of the graph.

Front

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

Back

The end behavior of a polynomial function can be determined by its degree and leading coefficient.

Front

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

Back

The leading term, which is the term with the highest degree, dominates the behavior of the polynomial for large values of x.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have up to n real zeros.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for x.

Front

What is the end behavior of the polynomial f(x) = 2x^3 - 4x + 1?

Back

As x approaches positive infinity, f(x) approaches positive infinity; as x approaches negative infinity, f(x) approaches negative infinity.

Front

What is a polynomial function with a positive leading coefficient and degree 4?

Back

An example is f(x) = x^4 - 3x^3 + 2x^2 + 1.