Alg1 Lesson 3.7: The Quadratic Formula

Lesson 3.7: The Quadratic

Formula

Obj: 6B, 8A, 10D, 10E, 10F, (11A): I can solve
quadratic equations using the quadratic formula.

EQ: How do I use the quadratic formula to solve
quadratic equations?

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

Roles:
Facilitator
Scribe
Resourcer
Includer

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 0: Square Roots

Solve Quadratic Equations by Taking Square Roots

Solve Quadratic Equations by Taking Square Roots

Part 1: Warming Up with the

Vertex Formula

f(x) = 2.4x² - 7.2x + 1.3

Vertex w/ Vertex Formula:

Graph:

X-Intercepts:

Drag and Drop

f(x) = 2.4x² - 7.2x + 1.3

Vertex: (​

Placeholder

, ​

Placeholder

)

X-Int: (​

Placeholder

, ​

Placeholder

) and (​

Placeholder

, 0)

Drag these tiles and drop them in the correct blank above

1.5

-4.1

0.193

0

2.807

1.3

2.4

Solve by Completing the Square

The literal
equation on the
right is used to
generalize solving
quadratics for all
cases. Once a
formula is
developed, the
algebra has been
done and all that
is left

Formulas

Once a formula is developed, the
algebra has been done and all that is
left is substituting the values and
performing the calculations.

Part 2: Deriving the
Quadratic Formula

Think about this formula derived from Part 1

This formula is helpful for quadratics in vertex form, but what
about quadratics in standard form? How could you use the
formula to solve a quadratic equation that is written out in
standard form?
Task: plug in the formulas for h and k into the x = formula.

Try using this formula to solve for the
zeros in the eq: f(x) = 2.4x² - 7.2x + 1.3

a = 2.4, b = -7.2, c = 1.3

Note: √39.36 doesn’t need
to be simplified since you
are not expected to
simplify square roots with
decimals inside of them.

Poll

Do you like math practice assignments on paper or online better?

• Paper

• Online

Part 3: Summary and

Practice

Two Important Conclusions:

● The quadratic formula can be used to solve any

quadratic equation.

● The quadratic formula is a logical result of
solving a quadratic equation that is written
in vertex form.

Handout 3.7 Practice with the Quadratic Formula

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.