Understanding Polynomial Functions and Their Properties

This lesson explores polynomial functions, including linear, quadratic, cubic, and quartic functions. It discusses their characteristics, roots, and end behavior. The lesson also covers how to match polynomial equations with graphs and use finite differences to determine the degree of a polynomial.

What is the leading coefficient of a linear function if it moves upwards from left to right?

• Less than zero

• Undefined

• Equal to zero

• Greater than zero

In which quadrants does a linear function with a positive leading coefficient start and end?

• Quadrant 1 to Quadrant 3

• Quadrant 4 to Quadrant 2

• Quadrant 3 to Quadrant 1

• Quadrant 2 to Quadrant 4

How many times can a quadratic function with a positive leading coefficient cross the x-axis at most?

• Three

• Two

• Four

• One

What shape does a quadratic function typically form?

• Line

• Ellipse

• Parabola

• Circle

What is the maximum number of roots a cubic function can have?

• Four

• Three

• Two

• One

If a cubic function has a negative leading coefficient, in which quadrants does it start and end?

• Quadrant 1 to Quadrant 3

• Quadrant 3 to Quadrant 1

• Quadrant 2 to Quadrant 4

• Quadrant 4 to Quadrant 2

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

• M shape

• W shape

• U shape

• V shape

How many times can a quartic function cross the x-axis at most?

• Five

• Four

• Three

• Two

What is the shape of a quartic function with a negative leading coefficient?

• W shape

• V shape

• U shape

• M shape

Which graph would a positive cubic function correspond to?

• First graph

• Second graph

• Fourth graph

• Third graph