Alg1 Lesson 3.6: Connecting Standard Form to Vertex Form

Lesson 3.6: Connecting

Standard Form to Vertex Form

Obj: 6B, (10A, 10B, 10C), 10D, 10E, 10F: I can convert quadratics to different forms.

EQ: How do I convert from vertex to standard form
and vice-versa?

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

Which one is the easiest role?

• Includer

• Resourcer

• Scribe

• Facilitator

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Practice Performance Task 3a:

The Catapult

Grading Conversion

Part 0: Linear and Quadratic

Function Operations

Multiple Choice

Simplify the expression.

x(x+5)-(x+5)

• x² + 4x - 5

• x² + 5x - 5

• x² - 5x + 5

• x² + 5x + 5

Multiple Choice

Simplify the expression.

7x(x-9)-2(x-9)

• 7x² + 36x + 18

• 7x² + 65x + 18

• 7x² - 36x + 18

• 7x² - 65x + 18

Multiple Choice

Simplify the expression.

x(2x - 3) - 4(2x - 3)

• 2x² - 14x + 12

• 2x² + 14x + 12

• 2x² - 11x + 12

• 2x² + 11x + 12

Multiple Choice

Simplify the expression.

-5x(x + 8) + 6(x + 8)

• -5x² - 34x + 4

• -5x² - 14x + 88

• -5x² - 8x + 4

• -5x² + 8x + 4

Multiple Choice

Find the product.

(x - 9)²

• x² - 9x + 90
• x² + 18x - 81

• x² - 9x + 81
• x² - 18x + 81

Multiple Choice

Find the product.

(2x + 1)(x - 6)

• 2x² + 5x - 6

• 2x² - 11x - 6

• 2x² - 5x + 6

• x² - 12x + 6

Multiple Choice

Find the product.

(3x + 1)²

• 9x² + 3x + 1
• 6x² + 2x + 1
• 3x² + 6x + 1
• 9x² + 6x + 1
• 9x² + 12x + 1

Labeling

Use the box method to find the product.

(x - 1)(x² + 2x + 8)

Drag labels to their correct position on the image

-2x

x

-1x²

+8

-1

+8x

+2x²

x²

+2x

Multiple Choice

Find the quotient.

$$\frac{2x^2+15x-8}{2x-1}$$

• x + 7
• 2x + 8
• x - 4

• x + 8

Multiple Choice

Find the quotient.

$$\frac{2x^2+15x+18}{2x+3}$$

• 2x + 9
• x + 9
• x + 3
• x + 6

Multiple Choice

Find the quotient.

$$\frac{5x^2-16x+3}{5x-1}$$

• x - 3
• 5x + 3
• x + 3
• 5x - 1
• x - 2

Multiple Choice

Find the quotient.

$$\frac{6x^2-11x-35}{3x+5}$$

• 2x + 5
• 2x - 5
• 3x - 7
• 2x - 7

Part 1: Warming Up with

Vertex Form

Standard to Vertex

Graph f(x) = 2x² - 4x + 5

Identify a and the vertex (h, k).

Write the equation in vertex form.

f(x) = a(x - h)² + k

Drag and Drop

Standard Form: f(x) = 2x² - 4x + 5

Factored Form: f(x) = ​

Placeholder

(x - ​

Placeholder

)² + ​

Placeholder

Drag these tiles and drop them in the correct blank above

2

1

3

4

5

8

Part 2: Developing

Formulas for the Vertex

How could you determine if these are the same function?

You can determine if they are the same by graphing or
converting the vertex form to standard form.

This Example

Generalized Example

Plugging in a, b, and c values from g(x) to find vertex.

Part 3: Summary and

Practice

Practice Using Formulas to Find the Vertex

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.