Download Extra Credit WORD Format

Algebra 2
Thanksgiving Holiday Extra Credit
Name_________________________ Pd____________
**Complete this ENTIRE WORKSHEET (Do Not Leave any blank) over the Holiday Break and turn in by 8:40am on
11/28/16 to receive up to 20 bonus points on the Unit 4 test based on how many you answer correctly and show work!!
You must Show all WORK to be graded! IT WILL NOT ACCEPT TED LATE... (Unless you have talked to me prior to the
break). Problems with a code (NW) require No Work. All others require you to show work!!
1.
Graph each parent function on the grid above the equation. (NW)
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
y
2.
2
4
6
8 10
-10 -8 -6 -4 -2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
3
2
4
6
8 10
2
4
6
8 10
y  2x
x
Graph each parent function on the grid above the equation. (NW)
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
y
2
4
6
8 10
-10 -8 -6 -4 -2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
y
x
Pg 1 of 12
1
x
3. Answer the following questions about the parent functions we studied. Write the name of the
function that meets the criteria asked: (NW)
a. Origin symmetry and No x-intercept.
_________________________
b. Domain (0, ) and Range (, ) .
_________________________
c. y-intercept (0,1)
_________________________
d. Domain is same as Range, with No symmetry
_________________________
4. Given the following solution graphed on the number line, write the solution in both Inequality
Notation and Interval Notation. (NW)
Inequality Notation (INQ): _________________________________________________
Interval Notation (INT): ___________________________________________________
5. Given the graph, write the domain and range in both formats. (NW)
Domain (INT): __________________________________
Domain (INQ): _________________________________
Range (INT): ___________________________________
Range (INQ): ___________________________________
Pg 2 of 12
6. Given the function f(x). LIST all the transformations in the correct order to f(x). (NW)
Function
Transformations (In Order)
a. 4 f ( x  3)  2
b.
1
f ( x  8)  5
3
1
c. f ( x  2)  7
2
d.
7.
4 f (4 x  4)  4
Given the graph of h(x) on the left grid, graph f(x) on the right grid using transformations. (2) NW
f ( x)  2h( x  3)  1
h( x )
Pg 3 of 12
8.
Given the graph of h(x) on the left grid, graph f(x) on the right grid using transformations. (2) NW
f ( x)  h(2 x  2)  1
h( x )
9. Find the inverse of the following function. Write your answer in the correct format if the inverse is a
function or not. (2)
f ( x)  3x  8
Inverse: ___________________________________
10. Find the inverse of the following function. Write your answer in the correct format if the inverse is a
function or not. (2)
f ( x)  x 2  25
Inverse: ______________________________________________________
Pg 4 of 12
11. Given the following graph of f(x), answer the following questions (a –c). There are no decimal
answers. (NW)
a.
f (7)  ________
b.
f (1)  ________
c.
f (9)  ________
12. Given the following functions f(x) and g(x) below, answer the questions (a – c)
f ( x)  6 x  4
a.
g ( x)  x 2  2 x
b. g ( 2)
f (3)
c.
f ( g (3))
13. Given the following functions f(x) and g(x) below, answer the questions (a – b). (2)
f ( x)  2 x  7
g ( x)  9 x  2
a.
Find
(f
g )(3)
b. Find
Pg 5 of 12
( g f )( x)
14. For the following equations, list the transformations on the line to assist you in graphing. Then
graph the equations with the transformations. Plot all points that will fit on the 10x10 grid. (2) NW
a.
y  2 |  x  4 | 3
Transf: _________________________
b. y  2 x  4  7
Transf: ____________________________
Pg 6 of 12
Solve each absolute value equation below. Check your answers for extraneous solutions. Show all steps
and work. Circle or box your final answers. (2)
15.
x  4  16  10
16. 3 x  3  4  44
Solve each absolute value inequality and then graph the solution set on the number line. Check for
extraneous solutions. (2)
17.
2 x  4  2  16
Solution: ___________________________
18.
2 | x  4 | 8  42
Solution: ______________________________
Pg 7 of 12
Questions 19-24: Factor the following quadratic equations. If it doesn’t factor, write Prime. NW
19.
x2 – 13x – 48
20.
16x2 – 1
21. 12x2 – 3x
Factors: ____________________
Factors: _____________________
Factors: __________________
22. 12x2 – x – 1
23. x2 – 7x + 6
24. 12 x 2  16 x  3
Factors: _________________
Factors: _________________
Factors: _________________
Questions 25-27. Simplify the following radical expressions: BOX your final answer!!
25.
28
26.
4 18
Pg 8 of 12
27.
6
48
Questions 28-31. Simplify the following complex number expressions: BOX your final answer!! (2)
28. (7  4i)  (12  11i)
29. (5  9i)  (13  12i)
30. (7  4i)(7  4i)
31. (6  2i )(5  9i)
Questions 32-34: Solve the following quadratic equations by the Square Roots method! Final answers
should be simplified radical. Put answers in box. (2)
32. 2x2 + 10 = 16
33. 3(x + 2)2 + 5 = -13
Pg 9 of 12
34. (x – 4)2 – 6 = 22
Questions 35-37: Solve the following quadratic equations by Completing the Square. Answers should be
simplified radical format. Put answers in box. (2)
35. x2 – 8x - 24 = 0
36. 2x2 – 16x + 44 = 0
37. x2 – 2x = 8
Questions 38-40: Solve the following quadratic equations using the quadratic formula.
x
b  b2  4ac
2a
Solve using the quadratic formula. Show all work! Reduce radicals if possible. Put final answers in the
box! (2)
38. 3x2 + 6x = -2
39. 6x2 – 8x + 3 = 0
Pg 10 of 12
40. 2x2 – x = -6
41. A rocket is fired at an angle and its path is modeled by the equation below. In the equation below
“h” is height in feet and “x” is horizontal distance in feet. Answer the questions below, using correct
units on answers. Round answers to 1 decimal place. (NW)
h  .0023x 2  4.65 x  5.3
a.
What was the maximum height of the rocket?
b.
At what horizontal distance did the rocket hit the ground from where it was launched?
c.
At what horizontal distances from launch was the rocket exactly 500 feet above the ground?
d.
What was the height of the rocket before it was fired into the air?
e. If there was a 100 feet high wall positioned 2000 feet horizontally from the rocket launch, would the
rocket make it over the wall? Explain your answer.
Questions 42-43: Graph the following quadratic inequalities. Then state the solution for each in Interval
Notation(INT). (2) (NW)
42.
y < -x2 – 5x + 3
43.
y ≥ 2x2 + 3x - 6
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
2
4
6
8 10
-10 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
Solution: _______________________
4
6
8 10
Solution: _________________________
Pg 11 of 12
Questions 44-45: Solve the Quadratic Inequalities below and graph your solutions on the number line
provided. Then write final solution in Interval Notation!!. Round to 1 decimal place. (2) NW
44. 2x2 – x – 6 > 0
45.
x2 – 6x ≤ 27
Soln: _______________________
Soln: ___________________________
Questions 46-47: Given the following 2 functions, prove whether or not they are inverses of one another
using composition. Show all work. (2)
46.
f ( x)  2 x  6
f ( x)  x  14
47.
g ( x)  14  x
Pg 12 of 12
g ( x) 
1
x 3
2