Download presentation

Presentation is loading. Please wait.

Published byMorgan Helin Modified over 2 years ago

1
**Special Equations : AND / OR and Quadratic Inequalities**

AND / OR are logic operators. AND – where two solution sets “share” common elements. - similar to intersection of two sets OR – where two solution sets are merged together - similar to union of two sets

2
**Special Equations : AND / OR and Quadratic Inequalities**

AND / OR are logic operators. AND – where two solution sets “share” common elements. - similar to intersection of two sets OR – where two solution sets are merged together - similar to union of two sets When utilizing these in graphing multiple inequality equations, a number line graph helps to “see” the final solution.

3
**Special Equations : AND / OR and Quadratic Inequalities**

AND / OR are logic operators. AND – where two solution sets “share” common elements. - similar to intersection of two sets OR – where two solution sets are merged together - similar to union of two sets When utilizing these in graphing multiple inequality equations, a number line graph helps to “see” the final solution. We will first look at how they are different.

4
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE :

5
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other

6
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each

7
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each 3. Find where they “share” elements - where are they “on top” of each other - in this case they share between (– 3) and 5

8
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each 3. Find where they “share” elements - in this case they share between (– 3) and 5 - where are they “on top” of each other 4. This shared space is our final graph

9
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE : - 3 5 Answer as an interval STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each 3. Find where they “share” elements - in this case they share between (– 3) and 5 - where are they “on top” of each other 4. This shared space is our final graph

10
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 2 :

11
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 2 : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other

12
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 2 : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each

13
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 2 : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each 3. Find where they “share” elements - where are they “on top” of each other - in this case they share numbers greater than 5

14
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each 3. Find where they “share” elements - where are they “on top” of each other - in this case they share numbers greater than 5 4. This shared space is our final graph

15
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE : - 3 5 Answer as an interval STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each 3. Find where they “share” elements - where are they “on top” of each other - in this case they share numbers greater than 5 4. This shared space is our final graph

16
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 3 :

17
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 3 : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other

18
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 3: - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each

19
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 3 : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each 3. Find where they “share” elements - where are they “on top” of each other - in this case they DO NOT share elements

20
**Ø Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 3 : Ø - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution set for each 3. Find where they “share” elements - where are they “on top” of each other - in this case they DO NOT share elements 4. SO we have An EMPTY SET

21
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 4 :

22
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 4 : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other

23
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 4 : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution for each

24
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 4 : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution for each 3. Now merge the two graphs and keep everything - this will be your answer

25
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 4 : - 3 5 Answer as an interval STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution for each 3. Now merge the two graphs and keep everything - this will be your answer

26
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 5 : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution for each

27
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 5 : - 3 5 STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution for each 3. Now merge the two graphs and keep everything - this will be your answer

28
**Special Equations : AND / OR and Quadratic Inequalities**

EXAMPLE # 5 : - 3 5 Answer as an interval STEPS : 1. Create a number line and locate your points. ( open circle for 5 and closed for – 3 ) - when graphing, graph one point higher than the other 2. Graph the solution for each 3. Now merge the two graphs and keep everything - this will be your answer

29
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point

30
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point Example # 1 : Graph the solution set for

31
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point Example # 1 : Graph the solution set for

32
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point Example # 1 : Graph the solution set for Open Circle - 2 3

33
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point Example # 1 : Graph the solution set for Open Circle FFFFFF TTTTTTTTTTTTTTT FFFFFF - 2 3

34
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point Example # 1 : Graph the solution set for Open Circle Answer as an interval ALWAYS graph the TRUE sections… FFFFFF TTTTTTTTTTTTTTT FFFFFF - 2 3

35
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point Example # 1 : Graph the solution set for

36
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point Example # 1 : Graph the solution set for

37
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point Example # 1 : Graph the solution set for Closed Circle - 4 - 3

38
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point Example # 1 : Graph the solution set for Closed Circle ALWAYS graph the TRUE sections… TTTTT FFFFF TTTTTTTTTTTTTTTTT - 4 - 3

39
**Special Equations : AND / OR and Quadratic Inequalities**

Graphing Quadratic Inequalities : Factor to find “critical points” ( where the equation = 0 ) 2. Locate your points on a number line 3. Pick a test point for TRUE or FALSE - true / false changes every time you pass a critical point Example # 1 : Graph the solution set for Closed Circle Answer as an interval ALWAYS graph the TRUE sections… TTTTT FFFFF TTTTTTTTTTTTTTTTT - 4 - 3

40
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Example # 1 : Graph the solution set for

41
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Next, multiply EVERYTHING by “x” and get all terms on one side… Example # 1 : Graph the solution set for

42
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Next, multiply EVERYTHING by “x” and get all terms on one side… Now just follow the steps as we did before… Example # 1 : Graph the solution set for Closed Circle -3 6

43
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Next, multiply EVERYTHING by “x” and get all terms on one side… Now just follow the steps as we did before… ** I like to test 1000 in these…because 18/1000 is very small, you can disregard it !!! Example # 1 : Graph the solution set for Closed Circle T F T F -3 6

44
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Next, multiply EVERYTHING by “x” and get all terms on one side… Now just follow the steps as we did before… ** I like to test 1000 in these…because 18/1000 is very small, you can disregard it !!! Example # 1 : Graph the solution set for Closed Circle ALWAYS graph the TRUE sections… T F T F -3 6

45
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Next, multiply EVERYTHING by “x” and get all terms on one side… Now just follow the steps as we did before… ** I like to test 1000 in these…because 18/1000 is very small, you can disregard it !!! Example # 1 : Graph the solution set for Closed Circle Answer as an interval ALWAYS graph the TRUE sections… T F T F -3 6

46
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Example # 2 : Graph the solution set for

47
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Next, multiply EVERYTHING by “x” and get all terms on one side… Example # 2 : Graph the solution set for

48
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Next, multiply EVERYTHING by “x” and get all terms on one side… Factor and get critical points… Example # 2 : Graph the solution set for Open Circle 3 5

49
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Next, multiply EVERYTHING by “x” and get all terms on one side… Factor and get critical points… Test 1000… Example # 2 : Graph the solution set for Open Circle T F T F 3 5

50
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Next, multiply EVERYTHING by “x” and get all terms on one side… Factor and get critical points… Test 1000… Example # 2 : Graph the solution set for Open Circle ALWAYS graph the TRUE sections… T F T F 3 5

51
**Special Equations : AND / OR and Quadratic Inequalities**

In some cases, the variable will be located in the denominator of a fraction. Since the denominator can not equal zero, zero instantly becomes a critical point with an open circle above it… Next, multiply EVERYTHING by “x” and get all terms on one side… Factor and get critical points… Test 1000… Example # 2 : Graph the solution set for Open Circle Answer as an interval ALWAYS graph the TRUE sections… T F T F 3 5

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on eco tourism in india Download ppt on festivals of france Download ppt on abdul kalam Ppt on technology in agriculture Ppt on effect of global warming on weather we like it or not Ppt on agriculture and food security Download ppt on brain chip technology Ppt on breast cancer awareness Mnt ppt on hypertension Paper presentation ppt on nanotechnology