Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra II Semester Exam Review Sheet
1. Translate the point (2, –3) left 2 units and up 3 units. Give the coordinates of the translated point.
2. Use a table to translate the graph 3 units to the left. Use the same coordinate plane as the original function.
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3. Identify the parent function for g (x) = (x + 3) and describe what transformation of the parent function it
represents.
4. Graph the data from the table. Describe the parent function and the transformation that best approximates the
data set.
x
y
–3
0
–2
1
1
2
6
3
13
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5. Let g(x) be the transformation, vertical translation 3 units down, of f(x) = −4x + 8. Write the rule for g(x).
6. Let g (x) be a vertical shift of f (x) = −x up 4 units followed by a vertical stretch by a factor of 3. Write the
rule for g (x) .
7. The data set shows the amount of funds raised and the number of participants in the fundraiser at the Family
House organization branches. Make a scatter plot of the data with number of participants as the independent
variable. Then, find the equation of the line of best fit and draw the line.
Family House Fundraiser
Number of participants
Funds raised ($)
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10 15 20 25 13 15 18
450 550 470 550 650 600 600 650
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8. An automotive mechanic charges $50 to diagnose the problem in a vehicle and $65 per hour for labor to fix
it.
a. If the mechanic increases his diagnostic fee to $60, what kind of transformation is this to the graph
of the total repair bill?
b. If the mechanic increases his labor rate to $75 per hour, what kind of transformation is this to the
graph of the total repair bill?
c. If it took 3 hours to repair your car, which of the two rate increases would have a greater effect on
your total bill?
9. Using the graph of f(x) = x 2 as a guide, describe the transformations, and then graph the function
g(x) = (x + 6) 2 − 2.
10. Find the minimum or maximum value of f(x) = x 2 − 2x − 6. Then state the domain and range of the function.
11. Find the zeros of the function h (x) = x 2 + 23x + 60 by factoring.
12. Solve the equation x 2 = 3 − 2x by completing the square.
13. Express 8 −84 in terms of i.
14. Find the zeros of the function f(x) = x 2 + 6x + 18.
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15. Consider the function f(x) = −4x 2 − 8x + 10. Determine whether the graph opens upward or downward. Find
the axis of symmetry, the vertex and the y-intercept. Graph the function.
16. Solve the equation 2x 2 + 18 = 0.
17. Find the zeros of f(x) = x 2 + 7x + 9 by using the Quadratic Formula.
18. Find the number and type of solutions for x 2 − 9x = −8.
19. Subtract. Write the result in the form a + bi.
(5 – 2i) – (6 + 8i)
20. Multiply 6i (4 − 6i) . Write the result in the form a + bi.
21. Simplify
−2 + 2i
.
5 + 3i
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22. Identify the degree of the monomial −5r 3 s 5 .
23. Rewrite the polynomial 12x2 + 6 – 7x5 + 3x3 + 7x4 – 5x in standard form. Then, identify the leading
coefficient, degree, and number of terms. Name the polynomial.
24. Add. Write your answer in standard form.
(5a 5 − a 4 ) + (a 5 + 7a 4 − 2)
25. Find the product (5x − 3)(x 3 − 5x + 2) .
26. Divide by using long division: (5x + 6x 3 − 8) ÷ (x − 2) .
27. Divide by using synthetic division.
(x 2 − 9x + 10) ÷ (x − 2)
28. Write an expression that represents the width of a rectangle with length x + 5 and area x 3 + 12x 2 + 47x + 60.
29. Make sure you study your vocabulary that is on your Semester Exam Review Learning Objective Sheet.
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ID: A
Algebra II Semester Exam Review Sheet
Answer Section
1. ANS:
TOP: 1-1 Exploring Transformations
2. ANS:
TOP: 1-1 Exploring Transformations
3. ANS:
The parent function is the cubic function, f (x) = x 3 .
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g (x) = (x + 3) represents a horizontal translation of the parent function 3 units to the left.
TOP: 1-2 Introduction to Parent Functions
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ID: A
4. ANS:
Square root function translated 3 units to the left.
TOP: 1-2 Introduction to Parent Functions
5. ANS:
g(x) = −4x + 5
TOP: 1-3 Transforming Linear Functions
6. ANS:
g (x) = −3x + 12
TOP: 1-3 Transforming Linear Functions
7. ANS:
y = 8.5x + 435.3; r ≈ 0.66
TOP: 1-4 Curve Fitting with Linear Models
8. ANS:
a. Vertical translation up 10
b. Horizontal compression by 13/15 or 0.867
c. The increase in labor rate.
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ID: A
9. ANS:
g(x) is f(x) translated 6 units left and 2 units down.
TOP: 2-1 Using Transformations to Graph Quadratic Functions
10. ANS:
The minimum value is –7. D: {all real numbers}; R: {y | y ≥ –7}
TOP: 2-2 Properties of Quadratic Functions in Standard Form
11. ANS:
x = −20 or x = −3
TOP: 2-3 Solving Quadratic Equations by Graphing and Factoring
12. ANS:
x = 1 or x = –3
TOP: 2-4 Completing the Square
13. ANS:
16i 21
TOP: 2-5 Complex Numbers and Roots
14. ANS:
x = –3 + 3i or –3 – 3i
TOP: 2-5 Complex Numbers and Roots
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ID: A
15. ANS:
The parabola opens downward.
The axis of symmetry is the line x = −1.
The vertex is the point (−1,14).
The y-intercept is 10.
TOP: 2-2 Properties of Quadratic Functions in Standard Form
16. ANS:
x = ±3i
TOP: 2-5 Complex Numbers and Roots
17. ANS:
x=
−7 ± 13
2
TOP: 2-6 The Quadratic Formula
18. ANS:
The equation has two real solutions.
TOP: 2-6 The Quadratic Formula
19. ANS:
–1 – 10i
TOP: 2-9 Operations with Complex Numbers
20. ANS:
36 + 24i
TOP: 2-9 Operations with Complex Numbers
21. ANS:
2
8
− 17 + 17 i
TOP: 2-9 Operations with Complex Numbers
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ID: A
22. ANS:
8
TOP: 3-1 Polynomials
23. ANS:
−7x 5 + 7x 4 + 3x 3 + 12x 2 − 5x + 6
leading coefficient: –7; degree: 5; number of terms: 6; name: quintic polynomial
TOP: 3-1 Polynomials
24. ANS:
6a 5 + 6a 4 − 2
TOP: 3-1 Polynomials
25. ANS:
5x 4 − 3x 3 − 25x 2 + 25x − 6
TOP: 3-2 Multiplying Polynomials
26. ANS:
50
6x 2 + 12x + 29 + (x − 2)
TOP: 3-3 Dividing Polynomials
27. ANS:
−4
x − 7+ x−2
TOP: 3-3 Dividing Polynomials
28. ANS:
x 2 + 7x + 12
TOP: 3-3 Dividing Polynomials
29. ANS:
Study vocabulary.
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