1. Simplify: (⁴√400)/(⁴√5) Show your work.

2. For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work.

y = -2x² + 2x +2

3. A manufacturer of shipping boxes has a box shaped like a cube. The side length is (5a + 4b). What is the volume of the box in terms of a and b? Show your work.

4. If a function, f(x) is shifted to the left four units, what will the transformed function look like?

5. Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $100. Show your work.

6. The velocity of sound in air is given by the equation = 20√(273. + t)   where v is the velocity in meters per second and t is the temperature in degrees Celsius. Find the temperature when the velocity is 329 meters per second by graphing the equation. Round the answer to the nearest degree. Show your work.

7. The volume in cubic feet of a box can be expressed as (x) = x³ - 6x² + 8x, or as the product of three linear factors with integer coefficients. The width of the box is x-2.

Factor the polynomial to find linear expressions for the height and the length. Show your work.

8. What is the solution to the equation √(2x +8) - 6 = 4. Show your work.

9. Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.

|4x +3| = 9 + 2x

x = _____ or _____

10. Write an expression for the volume of a cylinder with a height 7in. greater than the radius.

11. What is the value of log₈₁ 3? Show your work.

Time (hours) 0 1 2 3 4 5 6
Population (1000s) 5.1 3.03 1.72 1.17 1.38 2.35 4.08

12. In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.

Find a quadratic model for the data in the table. Type your answer below. Show your work.

13. Use the model from problem 12 to estimate the population of bacteria at 9 hours.

Type your answer below. Show your work.

14. Evaluate the expression for the given value of the variable(s). Show your work.

4(3h - 6)/(1 + h); h = - 2

15. Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.

16. Simplify the expression. Type your answer in the blank.

-(-13) = ___

17. Suppose you cut a small square from a square of fabric as shown in the diagram. Write an expression for the remaining shaded area. Factor the expression. Type your answer below.

18. Is the relation {(3, 5), (-4, 5), (-5, 0), (1, 1), (4, 0)} a function? Explain. Type your answer below.

19. Evaluate √7x (√x - 7√7) Show your work.

20. Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.

-3x⁵ + 9x⁴ + 5x³ + 3