U3L5: Solving Using the Zero Product Property

Warm Up Problems

Math Response

What is the answer to Warm Up #1?

Type answer here

Correct Answer: x^2+6x+8

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Math Response

What is the answer to Warm Up #2?

Type answer here

Correct Answer: x^2-4x+4

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Math Response

What is the answer to Warm Up #3?

Type answer here

Correct Answer: x^2-4

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Math Response

What is the answer to Warm Up #4?

Type answer here

Correct Answer: \left(x+2\right)\left(x+3\right)

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Math Response

What is the answer to Warm Up #5?

Type answer here

Correct Answer: \left(2x+3\right)\left(3x+1\right)

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Part 1 Group Work

​Today we are going to apply what we have learned so far about quadratics to learn how to solve quadratic equations.
With your partner answer the following questions.

Categorize

Options (7)

1x100

0x100

2x50

4x25

10x10

96x4

50x50

Organize these options into the right categories

Correct Solution

Incorrect Solution

Categorize

Options (8)

1x0

2x0

0x3

0x4

-2x2

-4x4

3x1

At least one of the factors (either a or b) must equal 0 in order for axb to = 0

Organize these options into the right categories

Correct Solution

Incorrect Solution

What do you notice?

Match

• a

• b

• c and d

• e

• f

? = 0

? = 0

? = 3

x = 2

x = 5 or

x = -2

• ? = 0

• ? = 0

• ? = 3

• x = 2

• x = 5 or

  x = -2

​Take Note

• What have you noticed when you are solving an equation with 2 factors equal to zero?
  At least one of the factors must be equal to zero!

• This is called the Zero Product Property

Part 2 Group Work

Math Response

What is the answer to part a?

Type answer here

Correct Answer: \left(x-6\right)\left(x+1\right)

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Drag and Drop

What is the answer to part b?

x=​ ​

Placeholder

or x=​

Placeholder

*Put the largest x-value first so it does not mark your answer incorrect

Drag these tiles and drop them in the correct blank above

6

-1

-6

1

0

Drag and Drop

2. Time to have some fun and make some more connections! Use your graphing calculator

and graph y = x² − 5x − 6 on the grid below (this is the graph provided!)

a. What are the x coordinates of the x-

intercepts?

​

Placeholder

​

Placeholder

*insert the smallest number first*

b. What are the y coordinates of the x

intercepts?​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

-1

6

0

-6

1

The x-intercepts are the solutions (or answers for what x should equal) because that is where y=0

Multiple Choice

Why is the zero product property important when solving quadratic equations?

• Because it allows us to solve equations by setting each factor to zero

• Because it helps us graph linear equations

• Because it is used to find the slope of a line

• Because it is only used in geometry

​Shade ABOVE the parabola for y-values GREATER than!

​You try this first and
then go to the next slide to check your answer!

​Shade BELOW the parabola for
y-values LESS than!

Math Response

When you write your equation be sure to start with f(x) =

Type answer here

Correct Answer: f\left(x\right)=\left(2x+1\right)\left(x-1\right)

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Multiple Select

Which of the following are steps to solve a quadratic by factoring?

• Rewrite the equation so it is set to zero

• Factor the quadratic equation

• Set each factor equal to zero and solve

• All of the above

Multiple Choice

According to the lesson summary, what must be true if a factored quadratic equation is equal to 0?

• At least one of the factors must be equal to zero

• Both factors must be positive

• The equation has no solution

• The equation must be linear

Work on the practice problems! We will check these at the start of class tomorrow.