End Behavior and Polynomial Properties

The video tutorial explains how to determine the end behavior of polynomials by analyzing the degree and leading coefficient. It emphasizes the importance of arranging polynomials in descending order of power and understanding whether the degree is odd or even, and if the leading coefficient is positive or negative. The tutorial also covers how to visualize end behavior through graphs and analyze the movement of graphs as x approaches positive or negative infinity. It concludes with a discussion on left and right hand behavior of graphs.

What is the first step in determining the end behavior of a polynomial?

• Determine the degree and leading coefficient

• Find the x-intercepts

• Calculate the derivative

• Identify the roots of the polynomial

What is the degree of a polynomial?

• The sum of the coefficients

• The highest power of the variable

• The number of terms in the polynomial

• The constant term

Why is it important to arrange polynomials in descending order?

• To simplify the polynomial

• To find the roots more easily

• To make the polynomial continuous

• To easily identify the leading coefficient and degree

What is the leading coefficient of a polynomial?

• The coefficient of the term with the highest power

• The coefficient of the constant term

• The sum of all coefficients

• The coefficient of the term with the lowest power

How can you determine if a polynomial's degree is even or odd?

• By checking the sign of the leading coefficient

• By counting the number of terms

• By finding the constant term

• By looking at the highest power of the variable

What does a positive leading coefficient indicate about the graph's end behavior?

• The graph will go down on the right end

• The graph will go up on the right end

• The graph will go up on both ends

• The graph will go down on both ends

What is the general shape of a graph with an odd degree and a positive leading coefficient?

• A curve going up on the left and down on the right

• A curve going down on the left and up on the right

• A parabola opening downwards

• A parabola opening upwards

What does the end behavior of a graph tell us?

• The exact shape of the graph

• The direction the graph heads as x approaches infinity

• The y-intercept of the graph

• The number of roots the graph has

As x approaches negative infinity, what happens to the graph if the leading coefficient is positive?

• The graph goes up

• The graph goes down

• The graph remains constant

• The graph oscillates

As x approaches positive infinity, what happens to the graph if the leading coefficient is positive?

• The graph goes up

• The graph goes down

• The graph oscillates

• The graph remains constant