Graphing Polynomials: Finding X Intercepts

This video tutorial teaches how to graph polynomials by finding X intercepts. It explains the importance of X intercepts, how they relate to the graph's factors, and the role of sign changes. The tutorial addresses common misunderstandings, such as the impact of squared factors, and guides viewers through the process of graphing by testing intervals. By the end, viewers will understand how to determine the graph's shape and direction based on the zeros of its factors.

What is the significance of X intercepts in graphing a polynomial?

• They show where the graph is undefined.

• They determine the Y intercepts.

• They help find the factors of the polynomial.

• They indicate the maximum points of the graph.

When does a polynomial graph change signs?

• When it passes through the X axis.

• When it reaches the end of the graph.

• At the Y intercepts.

• At the maximum points.

How does a squared factor affect the graph of a polynomial?

• It causes the graph to have a double root.

• It has no effect on the graph.

• It changes the Y intercept.

• It makes the graph linear.

What is the first step in graphing a polynomial?

• Calculating the maximum points.

• Finding the X intercepts.

• Determining the degree of the polynomial.

• Finding the Y intercepts.

How do you determine the sign of an interval between X intercepts?

• By checking the Y intercept.

• By testing a point within the interval.

• By looking at the graph's color.

• By calculating the derivative.

Why is it important to test all intervals when graphing a polynomial?

• To ensure the graph is continuous.

• To find the Y intercepts.

• To determine the sign changes accurately.

• To calculate the maximum points.

What should you do if a factor is squared in a polynomial?

• Treat it as a linear factor.

• Consider it as a double root.

• Use it to find the Y intercept.

• Ignore it as it has no effect.