أوراق عمل Solving Quadratic Equations by Factoring في الرياضيات باللغة الإنجليزية للصف الثاني عشر عام (2)

Solve each equation. Check your solutions. 1. x2 = 36

2. x2 = 81

3. (k + 1)2 = 9

4. 81 – 4b2 = 0

5. 3b(9b – 27) = 0

6. (7x + 3)(2x – 6) = 0

7. b2 = –3b

8. a2 = 4a

Solve each equation. Check your solutions. 9. x2 – 6x = 27

10. a2 + 11a = –18

11. n2 – 120 = 7n

12. d2 + 56 = –18d

13. y2 – 90 = 13y

14. h2 + 48 = 16h

15. x2 + 9x + 18 = 0

16. 4x2 + 28x + 49 = 0

Solve each equation. Check your solutions. 17. –9x2 = 30x + 25

18. –x2 – 12 = –8x

19. 36w2 = 121

20. 100 = 25w2

21. 64x2 – 1 = 0 23. b2 = 16

22. 4y2 – = 0 24. 81 – x2 = 0

25. Consider the equation c2 + 10c + 9 = 0. a. Solve the equation by factoring. b. Use the roots to sketch the related function.

26. Consider the equation x2 – 18x = –32. a. Solve the equation by factoring. b. Use the roots to sketch the related function.

27. NUMBER THEORY The product of the two consecutive positive integers is 11 more than their sum. What are the numbers?

28. LADDERS A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 feet, and the length of the ladder is one foot more than twice its distance from the wall. Find the distance from the wall to the bottom of the ladder. (Hint: Use the Pythagorean Theorem to solve the problem.)

29. FREE FALL The function f (t) = –16t2 + 576 represents the height of a freely falling ballast bag that was accidentally dropped from a hot air balloon 576 feet above the ground. After how many seconds t does the ballast bag hit the ground?

30. VOLUME Catalina can make an open-topped box out of a square piece of cardboard by cutting 3-inch squares from the corners and folding up the sides to meet. The volume of the resulting box is V = 3x2 – 36x + 108, where x is the original length and width of the cardboard. a. Factor the polynomial expression from the volume equation. b. What is the volume of the box if the original length of each side of the cardboard was 9 inches?

Write a quadratic function for the given graph.

Write a quadratic function that contains the given points.

35. (–9, 0), (–3, –30), (2, 0)

36. (–5, 0), (–4, 0), (3, 56)

37. (–4, 0), (2, –9), (8, 0)

38. (1, 0), (3, –18), (6, 0)

39. CONSTRUCT ARGUMENTS Kayla says the zeros of the equation 2m2 – 12m = 0 are 0 and –12. Is she correct? Explain your reasoning.

40. STRUCTURE Write an expression for the perimeter of a rectangle that has an area A = x2 + 20x + 96. Explain how you solved the problem.