1. (Put it on the back table under your class hour)
Get out your 3.2 Homework!
Extra Credit is DUE
(Put it on the back table under your class hour)
You will be able to determine the coordinates of the vertices of a region.
Today’s Objectives:

2. Warm Up Solve the system of inequalities. 𝒚>𝒙 2. 𝒚<−𝟒𝒙 3. 𝒙−𝒚≥−𝟏
𝒚>𝒙 𝒚<−𝟒𝒙 3. 𝒙−𝒚≥−𝟏
𝒚≥−𝒙 𝒚≥𝟑𝒙−𝟐 𝟐𝒙−𝒚≤𝟒

3. Finding Vertices
You can use graphing, elimination, and substitution to find the vertices of an enclosed region.

4. Step 1: Convert to Equations
An enclosed region is formed by three or more inequalities BUT to find the vertices we use systems of equations.
5𝑦≤2𝑥+10
𝑦≤−𝑥+9
9𝑦≥−2𝑥+9

5. Step 2: Graph
Begin solving for the vertices by graphing all three lines on the same coordinate plane.
5𝑦=2𝑥+10
𝑦=−𝑥+9
9𝑦=−2𝑥+9

6. 𝒚= 𝟐 𝟓 𝒙+𝟐
𝒚=−𝒙+𝟗
𝒚=− 𝟐 𝟗 𝒙+𝟏

7. Green & Yellow. Purple & Yellow. Green & Purple.
Step 3: Organize
You can use a chart to help organize your thoughts. Each system (#1, #2, #3) are based on an intersection on your graph.
Green & Yellow. Purple & Yellow. Green & Purple.

8. Step 4: Solve 5𝑦=2𝑥+10 𝑦=−𝑥+9 9𝑦=−2𝑥+9 Intersection was
found on the graph.
(5, 4)

9. Find the coordinates of the vertices of this system of inequalities.
Finding Vertices
Find the coordinates of the vertices of this system of inequalities.
4𝑦≥−15𝑥−32
𝑦≤− 1 4 𝑥+6
𝑦≥2𝑥−8

10. Find the coordinates of the vertices of this system of inequalities.
Finding Vertices
Find the coordinates of the vertices of this system of inequalities.
4𝑦=−15𝑥−32
𝑦=− 1 4 𝑥+6
𝑦=2𝑥−8

11. 𝑦= 15 4 𝑥−8
𝑦=− 1 4 𝑥+6
𝑦=2𝑥−8

12. Group Work Everyone will get a worksheet.
This worksheet is to be kept with your 3.2 notes.
Do not get ahead of me.
Help each other!!!!
A portion of the worksheet will be assigned as homework

13. You must complete 5 problems of your choice on the Vertices Worksheet
Homework…YAY! 
Lesson 3.2 Extension
You must complete 5 problems of your choice on the Vertices Worksheet