# Working Independently | The Advantages of Working Independently

I have completed this assignment myself; working independently and not consulting anyone except the instructor.

Multiple-choice: Select the correct answer and write it in the space provided.
Do not show work; write only one of the letters A, B, C, or D.

1. (4 pts) Solve using the Quadratic formula: . 1. Ans: __B__
2. 2
B.
C.
D.
3. (4 pts) Solve the equation:           2. Ans: __B___
4. B.
C.
D.
5. (4 pts) Solve the rational equation: . 3. Ans: ___A__
6. B.
C.
D.  No solution
7. (4 pts) Solve the rational equation: 4. Ans: _D__
8. 2
B. 3
C. 4
D. 5
9. (4 pts) Solve the inequality.
Write the solution using interval notation:                               5. Ans: __C__
10. B.
C.
D.
11. (4 pts) Find the minimum or maximum value of ,
and give the coordinates of the vertex of the parabola.
12. Ans: _C___
13. Maximum = 3; vertex (3, 4)
B. Maximum = 4; vertex (4, 3)
C.  Minimum = 4; vertex
D.  None of the above
14. (4 pts) Find the Vertex and indicate the direction that the parabola opens:
15. Ans: __B___
16. Vertex and Opens Up.
B. Vertex and Opens Up.
C. Vertex   and Opens Down.
D. Vertex   and Opens Down.
17. (4 pts) Simplify: 8. Ans: __C___
18. 1
B. -1
C.
D.
19. (4 pts) Multiply: . 9. Ans: __A__
20. B. 7
C.
D.
1. (4 pts) Express in the standard form : 10. Ans: __B__
2. B.
C.
D.
3. (4 pts) Find the Vertical Asymptote: 11. Ans: __B___
4. x=2
B. x=-2
C. x=-4
D. x=4
5. (4 pts) Find the Horizontal Asymptote: 12. Ans: _C____
6. x=2
B. x=-2
C. x=-1 (Should be y=-1)
D. x=1
7. 4 pts) Let f (x) = -2x3+4x2-x+1. Use the Intermediate Value Theorem to determine which interval must contain a zero of f(x).
1. Ans: __B___
2. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4
1. (4 pts) True or False: Let y=f(x) be a polynomial function. The x-intercepts of the function f(x) are the roots of the equation f(x) = 0.

14: Ans._____

1. (4 pts) True or False. Let y=f(x) be a polynomial function of degree 3.

The function y=f(x) must have at least one real root.                15. Ans: ____

1. (4 pts) True or False. It is possible for a quadratic equation with real coefficients to have one real and one complex root.
2. Ans: ____

## Working Independently | The Advantages of Working Independently

1. (6 pts) Consider the graph of the polynomial y=p(x). Answer the following questions. (No explanation needed)

(a) Is the degree of p(x) even or odd?                            Ans: _____

(b) Is the leading coefficient positive or negative?           Ans. ______

(c) How many real number zeros are there?                     Ans: ____

1. (15 pts) Let . (No explanations required)

(a)  State the y-intercept.

(b) State the x-intercept(s).

(c) State the vertical asymptote(s).

(d) State the horizontal asymptote.

(e) Draw the graph. Show the asymptotes.

1. (5 pts). Translate this sentence about area into a mathematical equation.

The area A of a regular hexagon is directly proportional to the square of the length s of its side.

1. (10 pts). Find all solutions, real and complex, of the equation x2-4x+5=0.

Simplify as much as possible and clearly show all the steps.