Polynomial Graphs

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 a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient is the coefficient of the term with the highest degree. It determines the end behavior of the polynomial graph.

Front

How do you determine the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero. They can be found by factoring the polynomial or using the quadratic formula.

Front

What is the significance of the degree of a polynomial in graphing?

Back

The degree of a polynomial affects the number of turning points and the end behavior of the graph.

Front

What is the difference between even and odd degree polynomials?

Back

Even degree polynomials have symmetric graphs about the y-axis, while odd degree polynomials have graphs that are symmetric about the origin.

Front

How can you identify the number of real zeros from the degree of a polynomial?

Back

A polynomial of degree n can have at most n real zeros.

Front

What is the general form of a cubic polynomial?

Back

A cubic polynomial can be expressed as f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

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

Back

The ends of the graph will rise in both directions (upward).

Front

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

Back

The left end of the graph will rise while the right end will fall.