Alg2 Lesson 1.7 Modeling Quadratic Vertex Form

Lesson 1.7: Modeling Data with

Quadratics in Vertex Form

Obj: I can formulate quadratic functions.

EQ: How do I formulate a quadratic equation in
vertex form?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas, vocab,

and prior knowledge

● 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 of the following best describes what you will do today?

• I will go to a small group with the teacher.

• I will display my screen as the main screen for my group.

• I will ask lots of questions to my peers, Remind, and the teacher.

• I will make sure our table is neat and orderly.

● Go to your calendar paper.

● Select a skill to work on.

● Work on Deltamath.

Remind each other at your group to do these:

Part 1: Maximizing the Area

of an Animal Pen

Handout 1.7.A

A farmer has 2,400 feet of fencing and needs to build a rectangular pen to fence in her

animals for grazing. The farmer hires you to help her determine the dimensions of the

pen enclosing the greatest area that can be constructed with the available fencing.

PART 1

1. Sketch at least three possible rectangular pens that use all the available fencing.

Write the dimensions of each rectangle in terms of width and length.

2. Create a three-column table for the width, length, and area of the animal pen.

Write the values from your three sketches into the table. Plot the points on a graph for
width x and area y.

3. Be ready to share your values with the class.

Word Cloud

Write a possible width, length, area you found for the 2,400 ft perimeter rectangle enclosing. (besides the example on the previous slide).

Example

Multiple Choice

What is the contextual domain of this quadratic model?

• 0ft < w < 1,200ft

• All Real Numbers

• All Integers

• Any Whole Nummber

• 0ft < w < 351,000ft

Multiple Choice

What types of situations can be appropriately modeled with quadratic functions?

• Area

• Projectile Motion

• Linear Rate of Change

• Gravity

• All of these

Factored Form Formula

A(w) = w(1200 - w)


Where w is the width and 1200-w is the length of the rectangular animal pen.

Part 2 of 1.7.A

1. Use Desmos to determine a quadratic regression equation in standard form for the
data set. Use the standard form formula y1 ~ ax1^2 + bx1 + c. How does this differ
from the factored form equation from the previous slide?

2. How can you use the regression equation and its graph to determine the dimensions
of the animal pen with the greatest area using the available fencing?

3. Use Desmos to find a regression equation in vertex form for the data set.
Use the formula y1 ~ a(x1 - h)^2 + k. How is this similar to and different from the
factored form formula A(w) = w(1200 - w) and the regression equation
you found in problem 1?

4. What is the vertex of the parabola? What is the maximum value of the quadratic
function? Interpret the meanings of the vertex of the parabola and the maximum value
of the quadratic function in the context of maximizing the area of an animal pen.
(Your description is the range of this model).

Write in your journal…

Part 2: Maximizing Fuel

Efficiency

Handout 1.7.B

Go to preap.org/Desmos-Fuel

Record observations about the data and construct a
scatterplot on the handout.

Quadratic Vertex Form Regression Formula:

y1 ~ a(x1 - h)^2 + k

Part 3: Writing Quadratic

Functions to Model Data Sets

Handout 1.7.C

Practice finding quadratic regressions using Desmos and use it to make predictions and state reasonable domain for the context.

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.

Open Ended

Answer the essential question: How do I formulate a quadratic equation in
vertex form?