Algebra IIFall Semester Final ReviewName______
Parent Functions
Match the parent functions with the graphs and write the name, domain, and range under each graph.
a. b. c. d. e. f.
1. 2. 3. 4.
5. 6.
Find the inverse of theequation.
7. 8.
Transformations
y = a (x - h) + k How does each transform the graph?
a - ______, h - ______, k - ______
Identify the parent function and describe the transformations:
9. 10. 11.
12. 13. 14.
Curve Fitting
Use the data provided in the table to answer each question.
x / - 1 / 0 / 1 / 2 / 3y / 10 / 8 / 6 / 4 / 2
15) What is the slope of the linear function?
16) Write the equation that represents the equation of best fit.
17) What will the value of y be when x is 10?
18) What is the correlation coefficient?
Use the data provided in the table to answer each question.
x / - 1 / 0 / 1 / 2 / 3y / - 6 / - 5 / - 2 / 3 / 10
19) Use finite difference to determine the type of polynomial function and write the equation of best fit.
20) What would be the value of y when x = 8?
The table provided shows personal income of Americans from 1998 – 2003. Let x = 0 represent the year 1990.
Year / Amount (trillions of dollars)1998 / 7.4
1999 / 7.8
2000 / 8.4
2001 / 8.7
2002 / 8.9
2003 / 9.2
(Source: U.S. Census Bureau. Statistical Abstract of the United States. 2004 -2005)
21) Assume the data is represented by a linear function. Write the equation of best fit.
22) Find the correlation coefficient.
Graphing Systems
Rules for graphing inequalities:
≤≥
Line:
Shade:
23. Graph the system of inequalities.24. Write the inequality that best describes the graph shown below?
25. Which graph best represents all the pairs of numbers (x, y) such that x + y < −6?
F G H J
Solving Systems by Substitution & Elimination
Explain what the following terms mean:
A. Independent systemB. Inconsistent systemC. Dependent system
Solve by substitution, elimination, or matrix operations:
26. 27.
28. 29.
30. In the system of equations 4x + 2y = 10 and 3x + 7y = -18, what expression can be correctly substituted for y in the equation 3x + 7y =-18?
31. Use substitution or elimination to solve these equations. Show your work
6x + y = -2
6x + 2y = 2
32. Use substitution to determine if the given ordered pair is a solution for the system of equations.
33. Juan bought 40 drinks, all either cola or root beer. The cola was equal to four times the number of cans of root beer. Write a system of equations and solve.
34. At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Write a system of equations and solve.
35. The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Write a system of equations and solve.
Matrix Problems
A = B = C =D =
36. 2A + B37. 2D – C38. AB39. DC40. det [A]
41. Solve
Unit 5 – Intro to Quadratics
To find axis of symmetry: To find vertex:
Find the axis of symmetry and vertex of the following. Show your work!!!
42. 2x2 – 4x + 543. x2 + 6x – 7
Find the roots/x-intercepts/zeros/solutions when y=0 from the graphs and tables below. (Write answer in ordered pair(s).)
44.
Find the following information for the given equation.
45. y = ¾ (x + 2)2 - 3
Opens:
AOS:
Vertex:
X-intercepts:
46. A ball is tossed straight up at a velocity of 64 ft/sec. The path of the ball is straight up and down. The height of the ball above the ground is modeled by the function h(x) = - 16 x 2 + 64 x. (Use your calculator to graph the path of the ball. Identify what you see
a. What are the coordinates for the maximum height of the ball?
b. What is the height of the ball at 3 seconds?______
c. Write the coordinates that represent the ball reaching the ground. ______
d. Explain what the x values represent in real life. ______
e. Explain what the y values represent in real life. ______
Factoring
Factor the following completely. Remember all types: simple table, split the middle, sum and difference of cubes, and grouping.
47. x2 – 5x + 648. x2 + 8x + 1549. x2 – 2550. x3 – 8
51. 64x3 + 125 (cube)52. 3xy + 15x – 4y – 2053. 16x2 – 454. x2 + 9x + 20
Solving Quadratic Equations
Find the solutions to the following quadratic functions. (Factor & Solve)
55. x2 – 1 = 056. x2 + 9x +14 = 0 57. x2 + 14x + 49 = 0
58. 5x2 + 7x + 2 = 059. 9x2 – 6x + 1 = 060. 4x – 12 = 0
Find the equation given the roots/zeros/x-intercepts:
61. x = -3, x = 562. x = -1/4, x = 263. x = 1/3, x = -7
For each question, identify the type and number of roots using the discriminant and then solve to find the roots.
64) -x2 - 5x + 665) 8x2 + 10x – 366) 3x2 − 4x – 1
# roots:# roots:# roots:
Type:Type:Type:
Solution:Solution:Solution:
Real World Applications of Quadratics
A rocket is shot straight up at a velocity of 128 ft/sec. The path of the ball is straight up and down. The height of the ball above the ground is modeled by the function h(t) = -16t2 + 128t. (Use your calculator to graph the path of the ball. Identify what you see on your calculator screen by finding the following. You can also use your table.)
67. What is the maximum height of the rocket?______
68. How long does it take for the rocket to reach its maximum height?______
69. How long until the rocket lands?______
Quadratic Forms
70) Place the functions in order from the widest to the narrowest.
y = 2x2y = x2 y = -5x2y = 0.3x2
71) Graph y = -(x + 2)(x – 3)72) Convert y = -5(x + 2)(x – 1) into standard form.
73) Convert y = x2 – 5x – 6 into factored form.74) Convert y = x2 + 8x – 10 into vertex form.
75) Find the length of the base and height of a triangle if the base is 2x + 4 and the height is x – 6 having an area of 48 u2.