# 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.

25 Problems : Solve for Real or Imaginary Roots, Word Problems (Sum of two numbers) , Lowest Terms, Inequalities and Quadratic Equations

1. Perform the indicated operation: (x3 - 2x2 - 4x + 3)  (x - 3)

2. Find the product: (x - 2)(x + 3)(x - 4)

3. Simplify without having negative exponents: (- 3s-3t2)-2

4. Convert to scientific notation and then solve. Give answer in scientific notation: (0.0000003)4

5. Factor completely: 3a3b - 3ab3

6. Factor completely: ax - 2a - 5x + 10

7. Solve: (2x - 1)(3x + 5) = 5

8. The sum of two numbers is 4, and their product is -32. Write the complete solution (no guessing or trial by error) and find the numbers.

9. Perform the indicated operation and write the answer in lowest terms:

10. Perform the indicated operation and write the answer in lowest terms:

11. Simplify:

12. Solve:

13. For a certain time period the ratio of the dollar value of exports to the dollar value of imports for the United States were 2 to 3. If the value of exports during that time period was 48 billion dollars, then what was the value of imports?

14. Simplify:

15. Simplify:

16. Simplify:

17. Find all real or imaginary solutions:

18. Find all real or imaginary solutions:

19. Two positive numbers differ by 11, and their square roots differ by 1. Write the complete solution (no guessing or trial by error) and find the numbers.

20. Solve by using the quadratic formula: 2x2 + 5x - 3 = 0

21. Solve by completing the square: 2x2 + x - 6 = 0

22. Solve by any method:

23. Graph the quadratic equation and state the domain and range: y = 16 - x2

24. Solve the inequality: w2 + 3w < 18. Also state (in proper interval notation) and graph the solution set.

25. Solve the inequality: . Also state (in proper interval notation) and graph the solution set.

On the attachment are 25 problems that need to be Solved completely in detail for me.

- Some may involve graphing.

- Also, they must be solved in Word using Equation Editor or similar. No hand written solving please, because I can not read scanned documents on my computer.

- Also, must be solved using Algebra concepts only, not Calculus or other methods.

Please see attachment more details to see if you can help.

THANKS!

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