Finding the Zeros and Multiplicity of a Quadratic Function

The video tutorial explains how to find the zeros of a polynomial function and determine their multiplicity. It reviews algebraic techniques for isolating variables, discusses factoring and simplification, and provides steps to solve for zeros. The concept of multiplicity is explained, highlighting its importance in graphing functions.

What is the significance of zeros in a polynomial function?

• They indicate the slope of the function.

• They are the points where the function equals zero.

• They are the points where the function is undefined.

• They represent the maximum points of the function.

What is the first step in solving for zeros of a polynomial function?

• Isolating the variable

• Calculating the integral

• Graphing the function

• Finding the derivative

When factoring a polynomial, what should you look for first?

• The coefficient of the leading term

• The highest degree term

• Common factors

• The constant term

Which pair of numbers is used to factor the trinomial in the example?

• 2 and 10

• 3 and 7

• 4 and 5

• 6 and 8

What does a multiplicity of two indicate about a zero on a graph?

• The graph will have a vertical asymptote at that point.

• The graph will have a horizontal asymptote at that point.

• The graph will bounce off the x-axis at that point.

• The graph will intersect the x-axis at that point.

How does multiplicity affect the graph of a polynomial function?

• It determines the number of turning points.

• It affects the steepness of the graph.

• It changes the domain of the function.

• It indicates how the graph interacts with the x-axis.

What is the multiplicity of a zero if the factor is squared?

• Two

• One

• Three

• Four