Name:___________________________________Date:_________________Period:________ 233 Honors Algebra 2

Unit 2 Review: Non-Calculator Graphing Quadratic Functions

• When a is between 0 and 1 the parabola is wide and when a is greater than 1 it is narrow.

• Standard Form: ax2 + bx + c ; To get the vertex use x = −b2a

and plug that in to find y.

• Vertex Form: a x − h( )2 + k ; The vertex is (h, k) Graph the quadratic using at least 5 points. 1. 32)( 2 −−= xxxf Circle: Opens Up or Down Wide or Narrow or Same

Vertex:___________

Axis of Symmetry Equation:_____

Maximum or Minimum:_________

y-intercept:___________

x-Intercepts:___________

2. f (x) = − 12(x − 3)2 + 5

Circle: Opens Up or Down Wide or Narrow or Same Vertex:___________

Axis of Symmetry:_____

Maximum or Minimum:_________

y-intercept:___________

x-Intercepts:___________

3. What is the vertex of y = 3x2 −12x + 4 ?

4. What is the minimum or maximum value of y = − 12x2 − 3x +1?

Solve Quadratic Equations by Factoring Solve by factoring the following quadratics. Set each equal to zero and check first for GCF! Note the following properties:

a. Difference of Two Squaresà ))((22 bababa −+=− b. Perfect Squareà 222 )(2 bababa +=++ and 222 )(2 bababa −=+−

5. 0782 =++ xx 6. 03692 =−− xx 7. x2 +10x = 24

8. 01092 2 =++ xx 9. 06135 2 =−+ xx 10. 016 2 =−− xx

11. 10x2 = 4x 12. 12x2 = 14x + 6 13. 12x2 − 60x + 27 = 0 14. 25x2 −16 = 0 15. 2x2 − 200 = 0 16. 0962 =+− xx Solve Quadratics using the Square Root Method

17. 12)1(3 2 =+x 18. − 23(x − 4)2 +1= −31 19. 5464 2 =+x

Solve Quadratics by Completing the Square 20. x2 −12x − 3= 0 21. x2 +10x −10 = 0

22. x2 − 5x + 9 = 0 23. x2 + x + 2 = 0 Solve Quadratics by Using the Quadratic Formula 24. 0322 =−+ xx 25. 0342 2 =+− xx

26. 0253 2 =−+− xx 27. 05103 2 =++ xx

28. 3x2 + 2x = 5 29. 2x2 = −3x − 6

Find the discriminant and determine the number and type of solutions.

30. 50202)( 2 −+= xxxf 31. 364)( 2 −= xxf 32. 1255)( 2 += xxf

Polynomial Operations

33. Subtract from 34. 4c3 − 3c2 + 2( )− −4c3 − 5c + 2( )

Simplify:

35. 2x3 − x + 3x2( ) x + 2( )

36.3x4 − 8( ) −5 − 2x2( )

37. x2 − 2y( )2 38. a − 2b( )3 39. 4x + 2y( )3

Factoring Polynomials

40. 41. 2ax + bx − 6ay − 3by

42. x3 − x2y − 4xy2 + 4y3 43. a2b2 − 4b2 − 25a2 +100

44. x3 − x2y − xy2 + y3 45. ay2 + by2 − a − b

x2 − 3x3 − x + 9x4 −x3 + 2x − 9x2 + 7

x4 − 2x3 −16x2 + 32x

46. x5 − 2x4 − x + 2 47. x3 − 512 48. −3c3 + 24 49. y4 − 81 50. 12a5 + 26a3 −10a 51. 6b4 −17b2 − 28 Solving Polynomials 52. x3 +1000 = 0 53. 27g3 − 8 = 0 53. p3 + 4 p2 − 9p = 36 54. 162y4 = 2

55. m6 − 64 = 0 56. 12n7 + 2n5 = 30n3 57. 16h5 − 25h3 + 9h = 0

Polynomial Division 58. 4x3 − 2x2 + 6x −1( ) ÷ 2x + 3( ) 59. 2x3 − 4x + 5( ) ÷ x + 4( ) 60. 6x4 − 9x3 −19x2 + 31x − 5( ) ÷ 2x2 + x − 5( ) 61. 3x4 − x2 + 6x( ) ÷ x − 3( ) 62. 4x + 2x3 + 7x2 −1( ) ÷ x +1( ) Given one factor of a polynomial, completely factor. 63. f x( ) = x3 + 9x2 − 37x −165 given x − 5 64. f x( ) = x4 − 4x3 + 8x − 32 given x − 4 65. f (x) = x5 − 3x4 − 4x3 + x2 − 3x − 4 given x +1 Find all solutions given one zero. 66. x3 + x2 −14x + 30 = 0;−5

Algebra 2 Honors Unit 2 Review – Calculator Section

1. Find the x-intercepts and the vertex: y = 12x2 + 5x −1

2. Find the roots of the quadratic and the axis of symmetry: y = −18x2 + 0.96x +18

3. Find the y-intercept and the x-intercepts: y = 0.86 x − 3( )2 − 1920

4. A ball is thrown upward with an initial velocity of 60 feet per second from a height of 8 ft. a. Write the equation representing this problem.

b. When will the ball be back to the ground?

c. When will the ball be at its highest point? How high will it be? 5. A skate park is a rectangle 100 ft long by 50 ft wide. The city wants to triple that area by adding the same distance x to the length and the width. Solve the quadratic to find the new dimensions of the skate park.

6. The Little Sluggers Little League uses a baseball-throwing machine to help train 5-year-old players to catch high pop-ups. It throws the baseball straight up with an initial velocity of 48 feet pet second from a height of 3.5 feet.

a. Write the equation that models the height of the ball t seconds after it is thrown.

b. What is the maximum height the baseball will reach? How many seconds will it take to reach that height?

c. When will the ball hit the ground?

7. A rectangular enclosure at a zoo is 35 feet long by 18 feet wide. The zoo wants to double its area by adding the same distance x to the length and width. Solve the quadratic. What are the new dimensions of the enclosure?

Solve completely using your Calculator: 8. 9x3 + 45x2 − 4x − 20 = 0 9. y = 3x4 +12x3 −16x2 − 4x + 5