Alg1 Lesson 3.9: Interpreting the Discriminant

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: Parabolas Without

x-intercepts

What are the x-intercepts of the graph of the
function f (x)= x² +1?

Does the equation x² + 1 = 0
have any real-number
solutions? Why or why not?

Use these when reasoning frequently!!

Solving f (x)= x² +1 using the Quadratic Formula

√-4 is NOT a real number!

Discriminant: The Value Inside the Square Root

Part 2: How Many

Solutions?

2 Imaginary Solutions

(No Real Solution)

b² - 4ac < 0

1 Repeated Real

Solution

b² - 4ac = 0

2 Unique Real

Solutions

b² - 4ac > 0

Discriminant = b² - 4ac

Handout 3.9: Practice Using the Discriminant

Set up each quadratic equation into the Quadratic
Formula. Identify the value of the discriminant and
state whether the equation has two unique real, one
repeated real, or two non-real solutions.

Part 3: Determining How

Many Intersections

Is it possible
to determine
the
intersection
points
algebraically,
and if so,
how?

Use substitution to set each quadratic expression equal to each other.

The x values of the intersections are x = 0.485 and x = 2.943

The discriminant > 0 and there are 2 intersection points.

What do you think would happen if the discriminant < 0 and if the discriminant = 0?

The discriminant
for both equations
together is negative
and there are no
intersections.

If the discriminant was
0, there would only be
1 intersection.

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.