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Tables

Site: Gladwin
Course: Michigan Algebra I Sept. 2012
Book: Tables
Printed by: Guest user
Date: Saturday, November 23, 2024, 5:07 AM

Description

Tables

Table of contents

Tables

Recall the table of values below from earlier in the unit. It demonstrates how tables that model a quadratic function have a common second difference. In order to model this function, use any of the three forms discussed earlier in the unit.

x

-2

-1

0

1

2

3

4

y

12

9

7

6

6

7

9



Example 1

Find the equation that models this table in standard form.

x

-2

-1

0

1

2

3

4

y

12

9

7

6

6

7

9

Step 1. Find the second difference.

x

-2

-1

0

1

2

3

4

y

12

9

7

6

6

7

9

TablesEx1-1

Step 2. Find the a-value.

The a-value is found by dividing the second difference by 2.

TablesEx1-2

Step 3. Find the c-value.

The c-value is the constant, or the point where y = 0.

In this table, c = 7.

Step 4. Find the b-value.

Substitute a and c into the equation and solve for b.

TablesEx1-3

Step 5. Substitute a, b and c into the equation.

TablesEx1-4

Example 2

Find the equation that models this table in factored form.

x

-2

-1

0

1

2

3

4

y

5

2

0

-1

-1

0

2

Step 1. Find the second difference.

x

-2

-1

0

1

2

3

4

y

5

2

0

-1

-1

0

2

TablesEx2-1



Step 2. Find the a-value.

The a-value is found by dividing the second difference by 2.

TablesEx2-2

Step 3 . Find the roots.

The roots of the table are the points where y = 0.
Therefore the roots of this table are (0, 0) and (3, 0).

Step 4 . Substitute a and the roots into the equation.

TablesEx2-3

Example 3

Find the equation that models this table in vertex form.

x

-2

-1

0

1

2

3

4

y

12

9

7

6

6

7

9

Step 1 . Find the second difference.

x

-2

-1

0

1

2

3

4

y

12

9

7

6

6

7

9

TablesEx3-1
Step 2. Find the a-value.

The a-value is found by dividing the second difference by 2.

TablesEx2-2

Step 3. Find the h-value.

The h-value is the x-coordinate of the vertex. Due to symmetry, the x-coordinate of the vertex is 1.5. Therefore, h = 1.5.

Step 4. Find the k-value.

Substitute a and h into the equation and solve for k.

TablesEx3-3

Step 5 . Substitute a, h and k into the equation.

TablesEx3-4

Video Lesson

To learn how to find a quadratic function given a table of values, select the following link:

Quadratics Tables and Functions

Using Calculator to Find Differences

To learn how to use a calculator to determine if a table represents a quadratic function (by finding the second difference), select the following link:

Calculator Practice

Guided Practice

To solidify your understanding of modeling quadratics using a table, visit the following link to Holt, Rinehart and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.

Guided Practice

Practice

Height of Triangles vs. Area Worksheet

Areas of Equilateral Triangles Worksheet

*Note: If Google Docs displays “Sorry, we were unable to retrieve the document for viewing,” refresh your browser.

Answer Keys

Height of Triangles vs. Area Answer Key

Areas of Equilateral Triangles Answer Key

*Note: If Google Docs displays “Sorry, we were unable to retrieve the document for viewing,” refresh your browser.

Note to teacher:  These worksheets and answer keys came from a lesson found on line.  The complete lesson with overview and teacher notes can be found at the following link.

Beginning Modeling for Linear and Quadratic Data

Sources

Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project

Holt, Rinehart & Winston, "Quadratic Functions ." http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch05_08_homeworkhelp.html (accessed 8/22/2010).

Holt, Rinehart & Winston, "Writing a Quadratic From Data." http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg2/player.html?contentSrc=7115/7115.xml (accessed 8/22/2010).

Macon State College, "Finding Differences." http://calculator.maconstate.edu/differences2/index.html #(accessed 08/05/2010).