More Polynomial Investigation

More Polynomial Investigation

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Review: Roots and Zeros

The roots of a polynomial function, p(x), are the solutions of the equation p(x)=0. Another name for the roots of a function is zeros of a function because at each root, the value of the function is zero. The real roots (or zeros) of a function have the same value as the x-values of the x-intercepts of its graph because the -intercepts are the points where the y-value of the function is zero.

Sometimes roots can be found by factoring and solving for p(x)=0.

Multiple Choice

Pictured is a third degree polynomial. What do you think is the maximum number of roots it can have?

• 0

• 2

• 3

• 4

Fill in the Blanks

What do you think is the maximum number of roots a polynomial of degree n can have?

Can a polynomial of n degree have fewer than n number of roots?

Multiple Choice

What is the minimum degree this polynomial can have?

• 4

• 1

• 2

• 5

You can use a number line to represent the -values for which a polynomial graph is above or below the x-axis. The bold parts of each number line below show where the output values of a polynomial function are positive. That is, where the graph is above the x-axis. The open circles show locations of the -intercepts or roots of the function. Where there is no shading, the value of the function is negative. Write a possible equation.

You can use a number line to represent the -values for which a polynomial graph is above or below the x-axis. The bold parts of each number line below show where the output values of a polynomial function are positive. That is, where the graph is above the x-axis. The open circles show locations of the -intercepts or roots of the function. Where there is no shading, the value of the function is negative. Write a possible equation. 

Positive

When the y-values of a graph get very large as the x-values get large, the graph has positive orientation. When the y-values of a graph get very small as the x-values get large, the graph has negative orientation.

Open Ended

Write a possible equation for the polynomial described by the number line.

Open Ended

Write a possible equation for the polynomial described by the number line.

Open Ended

What can you say about the graphs of polynomial functions with an even degree compared to the graphs of polynomial functions with an odd degree?

Triple Root