Graphs of Polynomials

Front

What is the end behavior of a polynomial function as x approaches -∞ and +∞?

Back

The end behavior describes how the function behaves as x approaches negative or positive infinity. For example, if the leading coefficient is positive and the degree is even, both ends rise to +∞.

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x that make the polynomial equal to zero. They are also known as the roots of the polynomial.

Tags

CCSS.HSF-IF.C.7C

Front

How do you find the zeros of the polynomial y = (x + 4)(x + 1)(x - 3)?

Back

Set each factor equal to zero: x + 4 = 0 (x = -4), x + 1 = 0 (x = -1), x - 3 = 0 (x = 3). The zeros are -4, -1, and 3.

Tags

CCSS.HSF-IF.C.7C

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient indicates the direction of the end behavior of the polynomial. If it is positive, the right end rises; if negative, the right end falls.

Front

Describe the end behavior of f(x) = -5x^4 - 2x^2 + 8.

Back

As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) also approaches -∞.

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 degree of a polynomial in its graph?

Back

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

Front

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

Back

A polynomial of degree n can have at most 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 difference between even and odd degree polynomials?

Back

Even degree polynomials have the same end behavior on both sides (both rise or both fall), while odd degree polynomials have opposite end behavior (one side rises and the other falls).