This document contains a series of math problems related to polynomials, including finding zeros, writing polynomials in standard form, graphing functions, and modeling data with polynomials. The problems cover topics like finding the vertex, axis of symmetry, and x-intercepts of quadratic functions; adding, multiplying, and dividing polynomials; and using polynomials to model real-world data with linear and quadratic regression.

2. 100 100 100 100 100 100
200 200 200 200 200 200
300 300 300 300 300 300
400 400 400 400 400 400
500 500 500 500 500 500
Hip to Be
Square
Zeroing-in
You’re
Imagining
Things
Asymptotes Just Draw
It
Super-
modeling

3. Find the vertex, axis of
symmetry, and x-intercepts of
f(x) = 3(x – 2)2
- 5
A 100

4. Vertex (2, 5)
Axis: x = 2
X-int: 2 5/3
A 100

5. Find the vertex, axis of
symmetry, and x-intercepts of
f(x) = -4(x + 1)2
- 3
A 200

6. Vertex: (-1, -3)
Axis: x = -1
No x-ints
A 200

7. Write the standard form of the
quadratic with vertex
(2, 3) that passes through (0, 2)
A 300

8. f(x) = -1/4(x – 2)2
+ 3
A 300

9. Write the standard form of the
quadratic with vertex (-1/4,
3/2) that passes through (-2, 0)
A 400

10. f(x) = -24/49(x + ¼)2
+ 3/2
A 400

11. Write the equation in
standard form, then find V,
A, and x-ints.
f(x) = 3 – x2
– 4x
A 500

12. F(x) = -(x + 2)2
+ 7
V: (-2, 7)
A: x = -2
X-int: -2 7
A 500

13. Find the real zeros of
–(x + 3)3
- 8
B 100

14. -8
B 100

15. Find a polynomial with zeros
of -2, 1, -1
B 200

16. x3
+ 2x2
– x - 2
B 200

17. Find the zeros of 2x3
+ 11x2
–
21x – 90 if one factor is x + 6
B 300

18. -6, -5/2, -3
B 300

19. Write a polynomial with
zeros of 1, -4, -3 + 5i
B 400

20. f(x) = x4
+ 9x3
+ 48x2
+ 78x - 136
B 400

21. Find the zeros of f(x) = x4
+
10x3
+ 26x2
+ 10x + 25
B 500

22. -5, -5, ± i
B 500

23. Write in standard form:
- -12 + 3
C 100

24. 3 – 2i 3
C 100

25. Write the result in standard
form: (1 + 6i)(5 – 2i)
C 200

26. 17 + 28i
C 200

27. Write in standard form:
6 + i
i
C 300

28. 1 – 6i
C 300

29. Write in standard form:
(4 – i)2
– (4 + i)2
C 400

30. -16i
C 400

31. Write in standard form:
1 – 7i
2 + 3i
C 500

32. -19 – 17i
13
C 500

33. Find all holes and VA of:
f(x) = x2
– 5x + 4
x2
- 1
D 100

34. VA: x = -1
Hole at x = 1
D 100

35. Find the holes and HA of:
f(x) = x2
– 3x – 8
x2
- 4
D 200

36. HA: y = 1
No holes
D 200

37. Find the holes, VA, and SA
of: f(x) = 2x3
+ 3x2
– 2x – 3
x2
– 3x + 2
D 300

38. VA: x = 2
SA: y = 2x + 9
Hole at x = 1
D 300

39. Find the holes, VA, HA, SA,
and intercepts of:
f(x) = 2x2
+ 7x + 3
x + 1
D 400

40. No holes
VA at x = -1
No HA
SA at y = 2x + 5
X-int: -1/2, -3
Y-int: 3
D 400

41. Find the holes, VA, HA, SA,
and intercepts of
f(x) = 3x2
+ 13x - 10
2x2
+ 11x + 5
D 500

42. Hole at x = -5
VA: x = -1/2
HA: y = 3/2
No SA
x-int: 2/3
y-int: -2
D 500

43. Graph f(x) = 2x – 1
x - 5
E 100

44. E 100

45. Graph f(x) = 2x
x2
+ 4
E 200

46. Correct Response
E 200

47. Graph f(x) = 2x – 10
x2
– 2x - 15
E 300

48. Correct Response
E 300

49. Graph f(x) = x2
– x + 1
x - 3
E 400

50. Correct Response
E 400

51. Graph f(x) = 2x3
+ x2
- 8x – 4
x2
– 3x + 2
E 500

52. Correct Respons
E 500

53. The value which helps you
determine how well a model
fits data
F 100

54. r2
F 100

55. The table shows the price per capita
consumption C (in pounds) of broccoli in the
US. Create a scatter plot.
F 200
Year Consumption
1999 6.2
2000 5.9
2001 5.4
2002 5.3
2003 5.7

56. What is t
F 200

57. A cubic model for the broccoli problem
is C = 0.0583t3
– 1.796t2
+ 17.99t –
52.7
Graph this with the scatter plot. Is it a
good fit? Explain.
F 300

58. What are ?
F 300

59. Give the quadratic model for
the broccoli problem. Is it a
good fit?
F 400

60. y = .129x2
– 2.99x + 22.76
No; r2
= .903 and it doesn’t
fit the graph well
F 400

61. Use the better model to
predict the broccoli
consumption in 2010.
F 500

62. 5.9 (from the cubic model)
F 500