Polynomial Characteristics Check

Front

What is a relative minimum in a polynomial function?

Back

A relative minimum is a point on the graph of a polynomial function where the function value is lower than the values of the function at nearby points.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values increase, the output values also increase.

Front

How do you find the zeros of a polynomial function?

Back

The zeros of a polynomial function are the values of x for which the function equals zero. They can be found by factoring the polynomial or using the quadratic formula.

Front

What are turning points in a polynomial function?

Back

Turning points are points on the graph where the function changes direction from increasing to decreasing or vice versa. They correspond to relative maximums and minimums.

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 a relative maximum in a polynomial function?

Back

A relative maximum is a point on the graph of a polynomial function where the function value is higher than the values of the function at nearby points.

Front

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

Back

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

Front

What is the difference between odd and even degree polynomials?

Back

Odd degree polynomials have opposite end behaviors (one end rises, the other falls), while even degree polynomials have the same end behavior (both ends rise or both ends fall).

Front

How can you determine the intervals where a polynomial function is increasing or decreasing?

Back

You can determine the intervals by analyzing the sign of the first derivative of the function.

Front

What is the y-intercept of a polynomial function?

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.