Determine end behavior of a polynomial

The video tutorial explains how to write a polynomial in standard form by arranging terms in descending order of exponents. It identifies the degree and leading coefficient of the polynomial, emphasizing their importance in determining the polynomial's end behavior. The tutorial uses the leading coefficient test to predict whether the polynomial's graph will rise or fall at the ends, focusing on even degree polynomials with positive leading coefficients. The explanation is applicable to various polynomial degrees, ensuring a consistent understanding of end behavior.

Why is it important to write a polynomial in standard form?

• To make it look neat

• To simplify calculations

• To identify the degree and leading coefficient

• To make it easier to graph

What is the degree of the polynomial 3x^2 + 6x?

• 6

• 1

• 2

• 3

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

• Both ends fall

• It forms a circle

• Both ends rise

• One end rises, one end falls

How does the degree of a polynomial affect its graph?

• It has no effect

• It determines the number of turns

• It changes the color of the graph

• It affects the width of the graph

What shape does a quadratic polynomial typically form?

• A square

• A parabola

• A circle

• A line