ALGEBRA 2 REVIEW

Give the slope of the line through the given points: (reduce fractions)

1. (0,0) and (-2, 6). __________ m =

2. (3,-1) and (0,2) __________ m =

3. (3,-2) and (6,-2) __________ m = this is a horizontal line

Zero divided by any nonzero value is zero

4. (2, 1) and 2, -7) __________ m = this is a vertical line

Never divide by zero but this will be more interesting as you move toward calculus

Choose from: slope, intercepts, parallel, coincide, intersect at one point to make the statement true.

5. Two lines that are parallel have the same _________ slopes

6. but different ______________ intercepts ( no common points)

7. Two lines that have the same slope and the same intercepts ______________ coincide, really one line with two equations

8. In a plane, if lines have different slopes, then they __________intersect at exactly one point

Give the slope and give the y-intercept for each given line.

9- m = __-2_

10- y-int__(0,8) _____

11- m = __-5__

12- y-int ___ (0,0) ____

Give the equation of the line with the given slope and y-intercept:

13. m = -4 and through (0, 3) ___________ y = -4x + 3

14. m = 2 and through (0, -5) ___________ y = 2x - 5

15. m = 1 and through (4, 4) ___________ y = x

16. m = -3 and through (0, 0) ___________ y=-3x

Give the equation of the line parallel to and through the given point:

17. (1,-1) _____y = x - 2 ________ y = x + b where x = 1 and y = -1 so -1 = 1 + b and b is -2

18. (3, 3) _____y = x ________ y = x + b where x = 3 and y = 3 so 3 = 3 + b and b is -0

Give the equation of the line parallel to and through the given point:

19. (1,-1) ____y = -2x +1 _________ y = -2x + b where x = 1 and y = -1 so -1 =-2* 1 + b and b is 1

20. (3, 3) _____y = -2x +9 ________ y = -2x + b where x = 3 and y = 3 so 3 = -2 * 3 + b and b is 9

Find the intersection of the given lines

21. and x = 4x-1 so x is 1/3 and y is 1/3

22. and (0,6)

True or False

23. _____ true

24. _____ true

25. _____ false y*y = y²

26. _____ true

Simplify

27. _____ 18

Compare using <, >, =

28. __<___

29. __<___

30. ___ < __

31. Graph on the number line.

32. Graph on the number line.

33. Write the appropriate inequalities following the pattern x – h, the shift from 6 is -5 so the inequalities are x > 1 or x < -11

34. Write the appropriate inequalities following the pattern x – h, the shift from 6 is -5 so the inequalities are x < 1 and x > -11

35. Give the 10^th term of the sequence: 5, 9, 13, 17, … arithmetic: you can see the common difference is 4 and the expression is 4n + 1 so you get 41 for the 10^th term

36. The gallons used varies directly with the miles driven. If it takes 18 gallons to drive 280 miles, how many gallons will it take to drive 450 miles?

Complete the square and write in vertex form.

37. _______________ half the middle term is 4 and 4 squared is 16;

38. _______________ half the middle term is -2 and -2 squared is 4;

37. _______________ half the middle term is 2.5 and 2.54 squared is 6.25;

Factor into two binomials.

40. = _______________ the factors of 9 are 1,3,9 and they can’t form a sum of 8; not factorable into integers
41. = _______________ product 48 and sum -19; (x - 16)(x - 3)
42. = ________________ product 4 and sum -5; (x – 4) ( x – 1)
43. = _________________ product 64 and sum 0; (x – 8) (x + 8)

Write as a simplified trinomial

44. = _________________ x² -10x+21

45. = ________________ 3x² + 15x + 2x + 10 = 3x² + 17x + 10

for

46. Identify a,b,c for use in the quadratic formula.. a = _2__ b = __-8_ c= __1__

47. Find the value of the discriminant. __72___
48. Find any roots. ___________________

Given the equation you should also be able to find the maximum height

49. Find if the initial height is7 ft and the initial velocity is 35 ft/sec. _______ at time 0 the height is the initial height of 7 ft
50. Find if the initial height is7 ft and the initial velocity is 35 ft/sec. _______ -16 *4 + 35 * 2 + 7 = -64 + 70 + 7 = 13