Graphing Polynomial Functions: End Behavior and Zeros

This video tutorial teaches how to graph polynomials by analyzing zeros, end behavior, and multiplicities. It covers three examples, starting with a polynomial in factored form, then factoring a polynomial to find zeros and multiplicities, and finally graphing a complex polynomial. The tutorial explains how to determine the end behavior using the leading coefficient and degree, and how multiplicities affect the graph's shape. The video also touches on finding y-intercepts and provides a brief introduction to more advanced topics like extreme values.

What is the first step in graphing a polynomial that is already in factored form?

• Find the zeros by setting each factor to zero

• Determine the end behavior

• Multiply all the factors

• Find the y-intercept

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

• The graph goes down to the left

• The graph goes up to the right

• The graph goes down to the right

• The graph goes up to the left

How does the end behavior of a polynomial with an odd degree behave?

• Both ends go up

• It forms a parabola

• Both ends go down

• One end goes up and the other goes down

What happens to the graph at a zero with a multiplicity of 2?

• It bounces off the x-axis

• It forms a cubic shape

• It forms a linear shape

• It passes straight through the x-axis

What shape does the graph take at a zero with a multiplicity of 3?

• It forms a parabola

• It bounces off the x-axis

• It passes straight through

• It forms a cubic shape

In Example 2, what is the first step in factoring the polynomial?

• Find the y-intercept

• Factor out the greatest common factor

• Determine the end behavior

• Set the polynomial to zero

What is the end behavior of the polynomial in Example 2?

• Down to the right, up to the left

• Up to the right, down to the left

• Both ends down

• Both ends up

In Example 3, what is the degree of the polynomial?

• 6

• 5

• 4

• 3

What is the end behavior of the polynomial in Example 3?

• Both ends go up

• Both ends go down

• It forms a cubic shape

• One end goes up and the other goes down

What shape does the graph take at a zero with a multiplicity of 1?

• It forms a cubic shape

• It forms a parabola

• It bounces off the x-axis

• It passes straight through