Polynomial Graphs

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

Front

What does it mean if a zero of a polynomial function has multiplicity 2?

Back

It means that the graph will 'bounce' off the x-axis at that zero.

Front

What is the factored form of a polynomial function?

Back

The factored form expresses the polynomial as a product of its linear factors, showing its zeros and their multiplicities.

Tags

CCSS.HSA.APR.B.2

Front

How do you find the minimum value of a polynomial graph?

Back

The minimum value can be found by identifying the lowest point on the graph, which corresponds to the vertex of the parabola in quadratic functions.

Tags

CCSS.HSF-IF.C.7A

Front

What are the zeros of the polynomial function f(x) = (x+2)(x-3)²(x-4)?

Back

The zeros are -2, 3 (with multiplicity 2), and 4.

Tags

CCSS.HSF-IF.C.7C

Front

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

Back

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

Front

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

Back

A polynomial with an odd degree will have opposite end behaviors; as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches negative infinity.

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 it can have, counting multiplicities.

Front

How can you determine the multiplicity of a zero from a graph?

Back

The multiplicity of a zero can be determined by observing how the graph behaves at that zero: it 'bounces' for even multiplicities and 'crosses' for odd multiplicities.

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.