Exploring Graphs of Polynomial Functions

The video tutorial covers polynomial functions, focusing on cubic, quartic, and quintic functions. It explains how to graph these functions, determine the number of real roots, and understand their behavior based on the leading coefficient. The tutorial uses Desmos for visualization and includes practice questions to reinforce learning.

What is the general shape of a cubic function when the leading coefficient is positive?

• It goes down, up, down.

• It goes up, down, up.

• It goes up, up, down.

• It goes down, down, up.

How many x-intercepts can a cubic function have at most?

• Three

• One

• Two

• Four

What happens to the graph of a cubic function when the leading coefficient is negative?

• It rotates 90 degrees.

• It flips left to right.

• It flips up and down.

• It remains the same.

What is the general shape of a quartic function when the leading coefficient is positive?

• It forms a W shape.

• It forms a V shape.

• It forms an M shape.

• It forms a U shape.

How many x-intercepts can a quartic function have at most?

• Four

• Five

• Three

• Two

What is the general shape of a quintic function when the leading coefficient is positive?

• It forms an M shape.

• It forms a W shape.

• It goes down, up, down, up, down.

• It goes up, down, up, down, up.

How many x-intercepts can a quintic function have at most?

• Three

• Four

• Six

• Five

What is the degree of a polynomial function with the highest exponent of 4?

• 5

• 4

• 3

• 2

What is the leading coefficient of the polynomial function 5x^4 + 3x^3 - 2x + 1?

• 5

• 1

• 3

• 4

What tool is recommended for graphing polynomial functions in the assignment?

• Excel

• Desmos

• Python

• Graphing calculator