End Behavior of Polynomial Function Graphs

The video tutorial explains polynomial functions, focusing on how the degree and leading coefficient influence the graph's shape. It covers the concept of polynomial degrees, showing how different degrees result in varying graph characteristics, such as bends. The leading coefficient's sign determines the graph's end behavior, with positive coefficients leading to upward trends and negative ones to downward trends. Examples illustrate these concepts, providing a comprehensive understanding of polynomial graphing.

What can we infer about a polynomial function by looking at its highest power term?

• The exact shape of the graph

• The number of zeros

• The y-intercept

• The general structure of the graph

What is the degree of the polynomial function P(x) = x^3 - 2x^2 + x + 5?

• 4

• 3

• 2

• 1

How many bends can a polynomial of degree 4 have?

• 1

• 2

• 4

• 3

What does a negative leading coefficient indicate about the graph of a polynomial?

• It will have a smiley face shape

• It will always be above the x-axis

• It will have a frowny face shape

• It will have no bends

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

• Always below the x-axis

• Always above the x-axis

• Starts low and ends high

• Starts high and ends low

If a polynomial has a degree of 5, how many bends can it potentially have?

• 2

• 5

• 3

• 4

What does the leading coefficient of a polynomial determine?

• The y-intercept

• The number of zeros

• The orientation of the graph

• The degree of the polynomial

What is the shape of a polynomial graph with an even degree and a positive leading coefficient?

• A straight line

• A parabola

• A smiley face

• A frowny face

How can you tell if a polynomial graph will have a 'happy' or 'sad' face?

• By looking at the leading coefficient

• By looking at the y-intercept

• By looking at the degree

• By looking at the number of terms

What is the general shape of a polynomial with an even degree and a negative leading coefficient?

• A parabola

• A straight line

• A frowny face

• A smiley face