Analyzing Polynomial Graphs

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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.

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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.

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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.

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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.

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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.

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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.

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What is an Absolute Minimum?

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

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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.

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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.

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

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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.