Alg1 Lesson 3.4: The Factored Form of a Quadratic

Lesson 3.4: The Factored

Form of a Quadratic

Obj: 6B, 7A, 7B, 10D, 10E, 10F: I can write quadratic
functions in factored form.

EQ: How do I factor a quadratic expression?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

What's your role today?

• Resourcer

• Facilitator

• Scribe

• Includer

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Part 1: Warming Up with

x- and y-intercepts

Multiple Choice

Can a linear function have exactly two x-intercepts?

• Yes

• No

Multiple Choice

Can a linear function have exactly two y-intercepts?

• Yes

• No

Part 2: Exploring Factored

Form

f(x)= (x − 2)(x +1)

Is this function linear or quadratic? How do you know?



How many x-intercepts does this function have?



What is the shape of this graph?



How many y-intercepts does this function have?

Drag and Drop

f(x)= (x − 2)(x +1)
The function ​

Placeholder

linear, because there are two linear factors.
There will be ​

Placeholder

x-intercepts since there are two values that make the factors equal to zero.
The shape of this function is a ​

Placeholder

.
There will be ​

Placeholder

y-intercept.

Drag these tiles and drop them in the correct blank above

is not

is

two

zero

parabola

umbrella

one

What do you notice
about the zeros in the
table and graph?

Multiple Choice

What do you notice about the two values of x that resulted in a zero?

• -2 and 3
• 0 and 1
• The x-values that resulted in a zero are -1 and 2.

Multiple Choice

What do you now know about the graph of this function?

• The graph has x-intercepts at x = -1 and x = 2, a y-intercept at y = -2, and a minimum at x = 0.5.
• The graph has x-intercepts at x = -1 and x = 2, a y-intercept at y = 1, and a minimum at x = 1.5.
• The graph crosses the x-axis at x = -1 and x = 3, a y-intercept at y = 2, and has no minimum value.
• The graph has x-intercepts at x = -2 and x = 1, a y-intercept at y = 0, and a maximum at x = 1.5.

Multiple Choice

What is the standard form of this quadratic function?

• f(x)= x² - 2x + 1

• f(x)= x² - 2x - 1

• f(x)= x² - x + 2

• f(x)= x² - x - 2

Part 3: Extend and Practice

Solve with Zero Product Property

Multiple Choice

How can we determine algebraically what value of x will make each factor zero?
Set each factor equal to zero.

• Set each factor equal to zero and solve for x.
• Use the quadratic formula and multiply by two.

• Factor the equation and set it equal to the constant coefficient.

• Set the equation equal to one and solve for x.

Multiple Choice

If f(x) = (2x - 1)(x+3), what are the zeros?

• x = 0 and x = -3
• x = 1 and x = 3
• x = -1/2 and x = 3
• x = 1/2 and x = -3

Multiple Choice

What is the y-intercept of f(x) = (2x - 1)(x+3)?

• (0, 1/2)

• (0, -3)
• (0, -1/2)

• (0, 3)

Graphing

Graph f(x) = 0.5(x - 1)(x+3)

Multiple Choice

What is the standard form of f(x) = (2x - 1)(x+3)?

• f(x) = 2x² - 4x - 3

• f(x) = 2x² + 4x - 3

• f(x) = 2x² - 5x - 3

• f(x) = 2x² + 5x - 3

Solve Quadratic Equations by Factoring

Multiple Choice

Answer the question.

• A.

• B.

• C.

• D.

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.