Tables
| Site: | Clare-Gladwin RESD |
| Course: | Michigan Algebra I |
| Book: | Tables |
| Printed by: | Guest user |
| Date: | Wednesday, January 15, 2025, 4:04 PM |
Description
Tables
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 |
Step 2. Find the a-value.
The a-value is found by dividing the second difference by 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.
Step 5. Substitute a, b and c into the equation.
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 |
Step 2. Find the a-value.
The a-value is found by dividing the second difference by 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.
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 |
The a-value is found by dividing the second difference by 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.
Step 5 . Substitute a, h and k into the equation.
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.
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).