# Word problems, Quadratic Equations and Inequalities

Word Problem

Diagonal Brace: The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures √6m. Find the width and height.

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Graph each parabola.

y = -1/3*(x^2) + 5

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Find the vertex and intercept for each parabola.

g(x) = x^2 +x-6

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Word problem

Maximum Height. If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t) = -16t^2 + 32t. When t is time in seconds, graph this parabola for 0 ≤ t ≤ 2. What is the maximum height reached by the ball?

NOTE to OTAs: Please help me with the above. I am having a hard time with all of them and I just want to make sure I can understand what I am doing so I can do it on my own with all the rest. The more steps you can provide me with the better. Thank you so much for any help youcan give me.

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#### Solution Summary

This solution shows how to graph the equations with all work and graphs formatted in an attached Word document.

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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