Graph Behavior and Intercepts

In this video, the teacher guides students through sketching a polynomial graph by using key concepts such as y-intercepts, x-intercepts, multiplicity, and end behavior. The process is verified using Desmos, and intervals are analyzed to ensure accuracy. The video emphasizes understanding the graph's behavior at different points and provides a step-by-step approach to sketching.

What is the main focus of the final section of the video?

• Calculating integrals

• Finding derivatives

• Sketching the graph

• Solving equations

What is the y-intercept of the graph discussed in the video?

• (0, 8)

• (0, -8)

• (0, 0)

• (0, -2)

Which of the following is an x-intercept of the graph?

• 1/2

• 3/4

• 2/3

• -1

What is the multiplicity of the x-intercept at -2?

• 4

• 3

• 2

• 1

How does the graph behave at an intercept with a multiplicity of 2?

• Forms a cusp

• Bounces off the axis

• Remains constant

• Crosses the axis

What is the end behavior of the graph?

• Starts above and ends below the x-axis

• Starts and ends below the x-axis

• Starts below and ends above the x-axis

• Starts and ends above the x-axis

Which tool is used to verify the graph sketch?

• GraphCalc

• Desmos

• Wolfram Alpha

• GeoGebra

What is the sign of the graph when x is less than -2?

• Undefined

• Zero

• Negative

• Positive

When x is between -2 and 2/3, what is the sign of the graph?

• Undefined

• Zero

• Negative

• Positive

What happens to the graph when x is greater than 2/3?

• It becomes undefined

• It remains zero

• It becomes positive

• It becomes negative