Analyzing Polynomial Graphs

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero. For example, if a polynomial has zeros at x = -1.5 and x = 1.5, these are the points where the graph intersects the x-axis.

Tags

CCSS.HSF-IF.C.7C

Front

How do you determine where a polynomial graph is increasing or decreasing?

Back

To determine where a polynomial graph is increasing or decreasing, analyze the x-values. A graph is increasing where the slope is positive and decreasing where the slope is negative.

Front

What does it mean if a section of the graph is decreasing?

Back

If a section of the graph is decreasing, it means that as the x-values increase, the y-values decrease. This indicates a negative slope in that interval.

Front

What is a Local Minimum on a polynomial graph?

Back

A Local Minimum is a point on the graph where the function value is lower than the values of the function at nearby points. It represents a local low point.

Front

What is a Local Maximum on a polynomial graph?

Back

A Local Maximum is a point on the graph where the function value is higher than the values of the function at nearby points. It represents a local high point.

Front

What is an Absolute Maximum?

Back

An Absolute Maximum is the highest point over the entire domain of the function. It is the largest value that the function reaches.

Front

What is an Absolute Minimum?

Back

An Absolute Minimum is the lowest point over the entire domain of the function. It is the smallest value that the function reaches.

Front

How do you find the relative maximum value of a polynomial?

Back

To find the relative maximum value, identify the highest point in a specific interval of the graph. This can be done by analyzing the critical points and evaluating the function at those points.

Front

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

Back

The y-intercept is the point where the graph intersects the y-axis. It represents the value of the polynomial when x = 0.

Front

What does it mean for a polynomial to have a degree of n?

Back

The degree of a polynomial is the highest power of x in the polynomial expression. It determines the number of zeros and the general shape of the graph.