Factoring Quadratic Functions and Zeros

This video tutorial explains how to factor quadratic functions to reveal their zeros. It covers the concept of zeros, their graphical representation, and the process of factoring by grouping. The tutorial also highlights common mistakes in factoring and provides a detailed example problem with a solution. By the end, viewers will understand how to rewrite quadratic functions in factored form to easily identify zeros.

What is the purpose of factoring a quadratic function?

• To make the function more complex

• To reveal the zeros of the function

• To change the function's degree

• To eliminate the x terms

What are the zeros of a function?

• The y-values that make the function zero

• The x-values that make the function zero

• The points where the function is undefined

• The maximum points of the function

What is the first step in factoring by grouping?

• Solving for x

• Graphing the function

• Checking for a common factor

• Finding the derivative

Which of the following is a common mistake when factoring?

• Graphing the function incorrectly

• Using the quadratic formula

• Choosing factors that do not sum to the middle term

• Ignoring the constant term

In the example, what are the two numbers that multiply to -84 and add to 17?

• 14 and -6

• 4 and -21

• 6 and -14

• 21 and -4

What is the zero product property used for?

• To determine the slope of a function

• To solve equations by setting each factor to zero

• To simplify complex numbers

• To find the maximum value of a function

What are the zeros of the function 5x^2 + 4x - 12?

• x = 5/6 and x = 2

• x = 6/5 and x = -2

• x = 2 and x = -3

• x = -5/6 and x = 2

How can you verify the zeros of a function?

• By finding the derivative

• By graphing the function

• By substituting the zeros back into the original equation

• By checking if the function is continuous

Why is it helpful to rewrite a function in factored form?

• It changes the degree of the function

• It reveals the zeros more clearly

• It makes the function more complex

• It eliminates the constant term

What is the result of substituting a zero into the function?

• The function equals the constant term

• The function equals the leading coefficient

• The function equals one

• The function equals zero