GRAPHING POLYNOMIAL FUNCTIONS 2

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

Front

What does the degree of a polynomial indicate?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. It indicates the polynomial's behavior and the maximum number of x-intercepts.

Front

How do you determine the x-intercepts of a polynomial function?

Back

To find the x-intercepts, set the polynomial equal to zero and solve for x. The solutions are the x-intercepts.

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the end behavior of the polynomial function. If it's positive, the graph rises to the right; if negative, it falls to the right.

Front

What is the difference between even and odd functions?

Back

An even function is symmetric about the y-axis (f(x) = f(-x)), while an odd function is symmetric about the origin (f(-x) = -f(x)).

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of each term, such as f(x) = ax^n + bx^(n-1) + ... + c.

Front

How do you convert a polynomial from factored form to standard form?

Back

To convert from factored form to standard form, multiply the factors together using the distributive property or the FOIL method.

Front

What is a root of a polynomial function?

Back

A root (or solution) of a polynomial function is a value of x that makes the function equal to zero.

Front

What is the relationship between the factors and roots of a polynomial?

Back

The roots of a polynomial correspond to the values of x that make each factor equal to zero. If (x - r) is a factor, then r is a root.

Front

What does the y-intercept of a polynomial function represent?

Back

The y-intercept is the point where the graph of the polynomial crosses the y-axis, found by evaluating the function at x = 0.