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Special Equations : AND / OR and Quadratic Inequalities AND / OR are logic operators. AND – where two solution sets “share” common elements. - similar.

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Presentation on theme: "Special Equations : AND / OR and Quadratic Inequalities AND / OR are logic operators. AND – where two solution sets “share” common elements. - similar."— Presentation transcript:

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 : 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 - 3 5

6 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE : 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 5

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

8 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE : 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 - 3 5

9 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE : 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 Answer as an interval

10 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 2 :

11 Special Equations : AND / OR and Quadratic Inequalities 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 EXAMPLE # 2 :

12 Special Equations : AND / OR and Quadratic Inequalities 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 EXAMPLE # 2 :

13 Special Equations : AND / OR and Quadratic Inequalities 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 EXAMPLE # 2 :

14 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE : 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 This shared space is our final graph

15 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE : 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 This shared space is our final graph Answer as an interval

16 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 3 :

17 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 3 : 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 - 3 5

18 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 3: 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 Graph the solution set for each

19 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 3 : 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 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 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 3 : 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 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 Ø

21 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 4 :

22 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 4 : 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 - 3 5

23 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 4 : 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 5

24 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 4 : 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 - 3 5

25 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 4 : 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 Answer as an interval

26 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 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 5

27 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 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 - 3 5

28 Special Equations : AND / OR and Quadratic Inequalities EXAMPLE # 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 Answer as an interval

29 Special Equations : AND / OR and Quadratic Inequalities Graphing Quadratic Inequalities : 1. 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 : 1. 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 : 1. 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 : 1. 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 - 23 Open Circle

33 Special Equations : AND / OR and Quadratic Inequalities Graphing Quadratic Inequalities : 1. 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 - 23 Open Circle TTTTTTTTTTTTTTTFFFFFF

34 Special Equations : AND / OR and Quadratic Inequalities Graphing Quadratic Inequalities : 1. 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 - 23 Open Circle TTTTTTTTTTTTTTTFFFFFF ALWAYS graph the TRUE sections… Answer as an interval

35 Special Equations : AND / OR and Quadratic Inequalities Graphing Quadratic Inequalities : 1. 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 : 1. 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 : 1. 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

38 Special Equations : AND / OR and Quadratic Inequalities Graphing Quadratic Inequalities : 1. 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 FFFFF TTTTTTTTTTTTTTTTTTTTTT ALWAYS graph the TRUE sections…

39 Special Equations : AND / OR and Quadratic Inequalities Graphing Quadratic Inequalities : 1. 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 FFFFF TTTTTTTTTTTTTTTTTTTTTT ALWAYS graph the TRUE sections… Answer as an interval

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 0

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 0

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

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 FTFT

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 FTFT ALWAYS graph the TRUE sections…

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 FTFT ALWAYS graph the TRUE sections… Answer as an interval

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 0

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 0

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 0 35 Open Circle

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 0 35 Open Circle F TT F

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 0 35 Open Circle F TT F ALWAYS graph the TRUE sections…

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 0 35 Open Circle F TT F ALWAYS graph the TRUE sections… Answer as an interval


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