Math

Name_________________________________ Quiz 4

Perform each of the following calculations involving complex numbers, and write the answer, simplified as much as possible, in the form a + bi, where a and b are real numbers. Show all work.

1. (4 pts)

2. (4 pts)

3. (4 pts)

4. (5 pts) Find the solutions of the equation . Simplify your answer as far as possible. Do not express your answer as a decimal Show work.

5. (2 pts each) Look at the graph and state the intercept(s), vertex, and range, and indicate which of equations A, B, C, or D, represents the graph. [ No explanations required.]

Graph	Fill in the blanks	Equation
	State the y-intercept: a.___________ State the x-intercept(s): b.____________ c.____________ State the vertex: d._____________ State the range: e.______________	The graph represents which of the following equations? f. Choice:_______ A. y = –x2 –2x +3 B. y = –x2 +2x + 3 C. y = x2 – 2x + 3 D. y = x2 +2x + 3

6. (4 pts each) Consider the equation .

(a) Find and state the value of the discriminant, b2 – 4ac . Then state whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exists. Show work.

(b) Find the exact solutions of the equation. Simplify as much as possible. Show work. You are welcome to use any of the techniques which apply and that you prefer except graphing (i.e., factoring, applying the principle of square roots, completing the square, or the quadratic formula).

7. At A water tank is being filled by water being pumped into the tank at a volume given by the formula, P(t) = 112t +2000 gallons per minute, where t is in minutes. At the same time the water tank has a leak and the volume of water draining out of the tank is given by the formula L(t) = 15t2 gallons per minute, where t is in minutes.

a.(2 pts) The volume, V, of water in the tank at any minute, t, is the difference of the volume of the water being pumped into the tank and the volume of water leaking out of the tank. Find the volume function, V(t).

b. (5 pts) The volume function is a quadratic function and so its graph is a parabola. Find the vertex of the volume function V(t). (Round answer to 1 decimal place) Show work.

c. (2 pts) Interpret the vertex in the context of the problem.

d. (5 pts) At what time (t > 0) will the tank be empty? Show work. (Round answer to 1 decimal place)

8. (6 pts) State the domain and then solve the equation. Show work.

9. (5 pts) Solve and write the solution in interval notation. Show work.

10. (4 pts) For f (x) = x4 – 3x2 − 8, use the Intermediate Value Theorem to determine which interval(s) must contain a zero of f.

Work/Explanation required 4. _______

A. Between 0 and 1

B. Between 1 and 2

C. Between 2 and 3

D. Between 3 and 4

11. (2 pts each) Each graph below represents a polynomial function. Complete the following table.

(no explanation required)

Graph
Is the degree of the polynomial odd or even? (choose one)	a.	b.
Is the leading coefficient of the polynomial positive or negative? (choose one)	c.	d.
How many real number zeros are there?	e.	f.

12. (2 pts each) Let.

(a) Write f(x) with the numerator and denominator completely factored.

(b) State the domain of f(x).

(c) State the vertical asymptote(s) of f(x

(d) State the horizontal asymptote f(x).

(e) State the y-intercept f(x).

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

13. (5 pts,) Solve the absolute value inequality and write your answer in interval notation for the solution set. Show all work.

|3x+5|≥4

14. (5 pts.) Solve the absolute value inequality and write your answer in interval notation for the solution set. Show all work.

|2 – 3x|<6