Alg1 Lesson 3.8: The Symmetry of the Parabola

Lesson 3.8: The Symmetry of

the Parabola

Obj: 6A, 7A, 7B: I can formulate quadratic functions
given the zeros.

EQ: How do I write a quadratic equation given it’s
x-intercepts?

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.

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Part 1: Connecting the

Intercepts and the Vertex

Drag and Drop

Given f(x) = 2x² - 12x - 14, find the
X value of the vertex. x = ​

Placeholder

The Factored Form: f(x) = 2(x+​

Placeholder

)(x-​

Placeholder

)

Drag these tiles and drop them in the correct blank above

3

1

7

5

6

9

Multiple Choice

The Factored Form: f(x) = 2(x+1)(x-7)
What are the x-intercepts?

• X-Int: (7, 0), (-1, 0)
• X-Int: (-7, 0), (1, 0)

• X-Int: (0, 7), (0, -1)
• X-Int: (0, -7), (0, 1)

Multiple Choice

What do you notice about the x-intercepts (blue pts) and the x-coordinate of the vertex (green pt)?

• The x-coordinate of the vertex is at the origin.
• The x-intercepts are located at the vertex.
• The x-intercepts are not related to the vertex.
• The x-intercepts are symmetrical since they are both 4 units away from the x value of the vertex.

Axis of Symmetry

a line that divides a parabola into mirror
images and passes through the vertex
(for quadratics, it will be in the x = h form)

Draw

Draw the other half of the butterfly.

Part 2: Connecting the

Quadratic Formula and the

Vertex

Practice Using the Quadratic Formula

Set up and solve

2x² - 12x - 14 = 0 using the
quadratic formula.

The Solutions are x = -1 and x = 7

What is the importance of the 3 ± 4 ?

x = 3 is the axis of symmetry. 4 is the distance
between the axis of symmetry and the
x-intercepts.

Part 3: Summary and

Practice

Handout 3.8: Practice with Parabolas

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.