Download Chapter 2 Unit Assessment (100pts)

Name:
Mrs. Hitzelberger
Date:
PCH/Period:
Chapter 2 Unit Assessment (100pts)
Part I Directions: Answer each in the space provided. Show all work.
You are not permitted to use a calculator for this section.
For Questions #1-7, answer the following questions about the given quadratic function:
f ( x )  2 x 2  12 x  16 .
1. Determine the function’s vertex. Give your answer in point form. ________________________
2. Is the function’s vertex a max or a min? __________________
3. Give the function’s axis of symmetry. _______________
4. Determine the function’s domain. Use correct notation. __________________
5. Determine the function’s range. Use correct notation. __________________
6. Identify the function’s x-intercept(s). _________________
7. Identify the function’s y-intercept(s). _________________
8. Determine the zeroes of the functions shown below. Show all work in the space provided.
a) f ( x)  9 x 4  25 x 2
b) f ( x)  x3  x 2  2 x
c) You are given the factor x  5 . Use long or synthetic division to determine all the zeros of the polynomial:
f ( x)  x3  6 x 2  7 x  60 .
Part II Directions: Answer each in the space provided. Show all work and circle your final
answer. Calculators are permitted for this section.
9. Divide the polynomial using long or synthetic division:
x
[A] x 2  8 x  13 
25
x2
[B] x 2  4 x  11 
21
x2
[C] x 2  8 x  13 
27
x2
[D] x 2  4 x  11 
9
x2
3
 6 x 2  3x  1   x  2 
10. Among all pairs of numbers whose sum is 14, find a pair whose product is as large as possible.
What is the maximum product?
1
[A] x  7
[B] x 
28
[C] x  49
[D] x  343
For Questions #11-14, refer to the word problem and function stated below:
The human cannonball is an act where a performer is launched through the air. The height of the performer can
2
be modeled by h( x)  0.007 x  x  20 , where h(x) represents the height in feet and x is the horizontal
distance traveled in feet.
11. What is the initial height of the person when he leaves the cannon?
[A] 20 feet
[B] 0 feet
[C] 55.71 feet
[D] 160.64 feet
12. What will be the person’s height (in the air) after traveling 2 feet?
[A] 20 feet
[B] 55.71 feet
[C] 21.97 feet
[D] 71.43 feet
13. Determine the maximum height of the human.
[A] 21.97 feet
[B] 71.43 feet
[C] 160.64 feet
[D] 55.71 feet
14. Oh no! The human missed the trampoline at the end of his act and is heading for the ground.
What is the total distance (from the start) traveled upon impact of the ground?
[A] 71.43 feet
[B] 160.64 feet
[C] 20 feet
[D] 142.86 feet
15. The function f ( x )   x 2  46 x  360 models the daily profit, f(x), in hundreds of dollars, for a
company that manufactures x computers daily. How many computers should be manufactured each day
to maximize profit? What is the maximum daily profit? Be sure to label each of your answers!
Use the function, f ( x )  x 
3
, to answer questions #16-20.
2x  5
16. Rewrite the function with a common denominator.
17. Determine the x-intercept(s) of the rational function above.
18. Determine the y-intercept of the rational function above.
19. Determine the vertical asymptote of the rational function above.
20. Determine the horizontal asymptote of the rational function above.
2x2  9x  4
21. Determine the slant asymptote of the function, f ( x) 
.
x3
22. Which of the following is a possible rational function that meets the criteria given below?
x-intercept: x=-2; Vertical Asymptote: x = 5; Slant Asymptote: y=x+3
[A] y 
x5
x3
x2  2x  8
[B] y 
x5
x2  2x  8
[C] y 
x3
x 2  2 x  15
[D] y 
x5
Use the following description to answer questions #23-24.
A company is planning to manufacture portable satellite radio players where the cost function,
C ( x)  10 x  3000 , can be used to model how their production costs. The fixed monthly cost will be $3000
and it will cost $10 to produce each player.
23. Determine the average cost to produce 150 satellite radio players.
[A] $3,150
[B] $1,500
[C] $30
[D] $4,500
24. What is the horizontal asymptote for the average cost function?
[A] 3,000
[B] 10
[C] 150
[D] 0
Bonus:
Using y  a( x  h) 2  k , write the quadratic equation that has the vertex (-4, -12) and a
point (-1, -15) on the parabola.