Graphs of Polynomials

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.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How does the degree of a polynomial affect its graph?

Back

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

Front

What is the degree of the polynomial f(x) = ⅝x³ + 2x²?

Back

The degree of the polynomial is 3, as the highest power of x is 3.

Front

What does a negative leading coefficient indicate about the graph of a polynomial?

Back

A negative leading coefficient indicates that the graph will fall to the right as x approaches positive infinity.

Front

What does a positive leading coefficient indicate about the graph of a polynomial?

Back

A positive leading coefficient indicates that the graph will rise to the right as x approaches positive infinity.

Front

What are the x-intercepts of a polynomial function?

Back

The x-intercepts are the points where the graph of the polynomial crosses the x-axis, corresponding to the roots of the polynomial.

Front

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

Back

The y-intercept is the point where the graph crosses the y-axis, representing the value of the polynomial when x=0.

Front

How can you determine the end behavior of a polynomial function?

Back

The end behavior can be determined by the leading coefficient and the degree of the polynomial.

Front

What is the relationship between the degree of a polynomial and the number of roots it can have?

Back

A polynomial of degree n can have up to n roots, counting multiplicities.