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Graphing and Solving Quadratic Inequalities (3 Problems)

State the solution set using interval notation and graph the solution set.

Please check these for me and graph them.
I do not know how to use a graphing tool.
If you also have any advice on how & what tool I can use to graph, it would be helpful.
Please do not handwrite the Graphs because I can not view scanned photos on my computer. Thanks a lot.

Quadratic inequalities.
State the solution set using interval notation and graph the solution set.

p.569 #12

a>0 or x<-2

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State the solution set using interval notation and graph its solution set .

Note : They have only asked for graph of the solution set ( which is basically a number line denoting the set of real numbers ) and not for the graph of the expressions given .

12. Given x2 + x > 0  x ( x + 1 ) > 0

Rule (i) : a . b = + ve then either both ' a ' and ' b ' got to be positive or
negative .

Numerical example : 2 times 3 = 6 or (-2 ) times ( -3 ) = 6

That makes :

x > 0 or x + 1 > 0

consider x + 1 > 0 , subtract 1 from both the sides to get : x > - 1

 x > 0 or x > -1

common region : x > 0

Writing it in mathematical notation , we have : x in ( 0 ,  )

x < 0 or x + 1 < 0

consider x + 1 < 0 , subtract 1 from both the sides to get : x < - 1

 x < 0 or x < - 1

common region : x < - 1

Writing it in mathematical notation , we have : x in ( -  , -1 )

Note : open brackets means the set doesn't include the end points . Infinity denoted by '  ' stands for the extreme point or the maximum end value in the number line , the set of real numbers .

 so the solution our given expression is ( -  , - 1 ) U ( 0 ,  )

graph of this solution set is as given below :

Note : circle in the graph ...

Solution Summary

Quadratic inequalities are solved and graphed. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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