Graphing Polynomials: Key Concepts and Techniques

This video tutorial covers the basics of polynomials, including their degrees and leading coefficients. It explores parent functions and graphing techniques, focusing on end behavior and transformations. The tutorial also delves into identifying zeros and understanding multiplicity, as well as factoring polynomials to solve for zeros. Throughout, the use of graphing calculators is emphasized to visualize and analyze polynomial functions.

What is the degree of a constant polynomial?

• 0

• 1

• Undefined

• Infinite

What is the leading coefficient of a polynomial in standard form?

• The constant term

• The coefficient of the term with the highest degree

• The sum of all coefficients

• The coefficient of the x term

What is the degree of a polynomial function that has a term x^5?

• Undefined

• 6

• 4

• 5

What does the end behavior of a polynomial function describe?

• The number of zeros in the polynomial

• The behavior of the graph as x approaches positive or negative infinity

• The coefficients of the polynomial

• The highest degree of the polynomial

What does the graph of a constant function look like?

• A vertical line

• A horizontal line

• A cubic curve

• A parabola

How is the turning point of a polynomial graph defined?

• Where the graph changes direction

• The lowest point on the graph

• Where the graph intersects the x-axis

• The highest point on the graph

What is the multiplicity of a zero that the graph touches but does not cross?

• Even

• Zero

• Odd

• Prime

How many real zeros can a cubic polynomial function have at most?

• 4

• 1

• 2

• 3

If a polynomial function has a zero at x = -4 with a multiplicity of 3, what does the graph do at x = -4?

• Touches the x-axis but does not cross

• Reaches a maximum or minimum

• Touches and crosses the x-axis

• Has a turning point

If a polynomial function's graph has a zero at x = 2 that it bounces off from, what is the multiplicity of this zero?

• 1

• 3

• 2

• 0