Graphing Polynomials Review

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. For example, for the polynomial p(x) = x^2 - 3x + 2, the zeros are x = 1 and x = 2.

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. For example, in the polynomial 4x^3 + 2x^2 - x + 5, the leading coefficient is 4.

Front

How do you determine the intervals where a polynomial is increasing?

Back

To determine where a polynomial is increasing, find the derivative of the polynomial and identify the intervals where the derivative is positive.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 3x^4 - 2x^2 + 1, the degree is 4.

Front

What does it mean for a polynomial to have an even degree?

Back

A polynomial has an even degree if the highest exponent of the variable is an even number. Even degree polynomials have the same end behavior on both sides of the graph.

Front

What does it mean for a polynomial to have an odd degree?

Back

A polynomial has an odd degree if the highest exponent of the variable is an odd number. Odd degree polynomials have opposite end behavior on both sides of the graph.

Front

How can you identify the end behavior of a polynomial?

Back

The end behavior of a polynomial can be determined by the leading term. If the leading coefficient is positive and the degree is even, the ends rise. If the leading coefficient is negative and the degree is even, the ends fall.

Front

What is the significance of the y-intercept in a polynomial graph?

Back

The y-intercept of a polynomial graph is the point where the graph crosses the y-axis. It can be found by evaluating the polynomial at x = 0.

Front

How do you find the x-intercepts of a polynomial?

Back

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

Front

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

Back

The degree of a polynomial indicates the maximum number of zeros (real or complex) it can have. For example, a polynomial of degree 3 can have up to 3 zeros.