Understanding Zeros of a Cubic Function

The video tutorial explains how to find the zeros of a cubic function by solving the equation using the factoring by grouping technique. It demonstrates the process of factoring the expression, solving for zeros, and rationalizing the denominator. The tutorial also includes a graphical verification of the solutions using Desmos, highlighting the x-intercepts as the zeros of the function.

What is the primary goal when finding the zeros of a cubic function?

• To find the x-values that make the function equal to zero

• To find the minimum value of the function

• To find the maximum value of the function

• To find the y-values that make the function equal to zero

What is the first step in factoring by grouping?

• Combine all terms into a single expression

• Cut the expression in half and factor each part

• Multiply all terms by the greatest common factor

• Add a constant to both sides of the equation

When factoring by grouping, what should you do if you have a negative sign in front of a term?

• Add a positive one

• Factor out a negative one

• Ignore the negative sign

• Multiply by two

After factoring the expression, what equation do you solve to find one of the zeros?

• x + 3 = 0

• 2x + 1 = 0

• x - 3 = 0

• 2x - 1 = 0

What is the result of solving the equation x - 3 = 0?

• x = -3

• x = 0

• x = 3

• x = 1

How do you rationalize the denominator of 1 divided by the square root of 2?

• Divide by 2

• Add the square root of 2

• Multiply by 2

• Multiply by the square root of 2

What are the two real irrational zeros of the function?

• Negative square root of 2 and positive square root of 2

• Negative square root of 2 divided by 2 and positive square root of 2 divided by 2

• Negative 2 and positive 2

• Negative 1 and positive 1

What tool is used to graphically verify the zeros of the cubic function?

• Calculator

• Graph paper

• Excel

• Desmos

What does the ordered pair (3, 0) represent on the graph?

• A maximum point

• A minimum point

• A zero of the function

• A point of inflection

What does the graph show about the irrational zeros?

• They are incorrect

• They are exact values

• They are approximations

• They are not visible