Intro to Analyzing Polynomial Graphs

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 degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What are x-intercepts?

Back

X-intercepts are points where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

What is end behavior in polynomial graphs?

Back

End behavior describes how the values of a polynomial function behave as the input (x) approaches positive or negative infinity.

Front

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

Back

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

Front

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

Back

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

Front

What is a turning point in a polynomial graph?

Back

A turning point is a point where the graph changes direction from increasing to decreasing or vice versa.

Front

How do you determine the number of turning points in a polynomial?

Back

The maximum number of turning points in a polynomial function is one less than the degree of the polynomial.

Front

What is the significance of the factor (x + 1) in a polynomial?

Back

The factor (x + 1) indicates that the graph will have an x-intercept at x = -1.

Front

What is the relationship between the degree of a polynomial and the number of x-intercepts?

Back

A polynomial of degree n can have up to n x-intercepts, but not all x-intercepts need to be real.