PreAP Algebra II
2nd Quarter Review
Name___________________________________
Date_______________________ Period_______
Find the zeros of the following functions:
1.
f(x) = x2 + 14x + 49
3. 4x2 – 20 = 5
2. f(x) = x2 + 8x + 21
4. 8x = x2 + 1
6. Solve: (x – 7)2 = 36
5.
What are the roots for 5 x 2 + 6 x + 5 = 0 ?
7.
Solve the inequality x2 + 13x + 45 < 5 using any method.
8.
State the discriminant for 2x2 – 3x = 4. Give the number and type of solutions.
Factor completely.
9.
x3 + 27
10. 64x3 + 16xy2 – 8x2y + 8
11. 8ax – 6x – 12a + 9
12. 16 x 5 y − 54 x 2 y 4
Give the product.
13. (2x – 1)(3x2 + 2x – 5)
14. (4x + y)3
15. Complete the square for the expression x2 – 18x + ______.
16. Complete the square for the expression x2 – 5x + ______. Give as a binomial squared. __________
17. y = x2 – 4x + 3
Vertex: ____________
Axis of Symmetry: ________________
Max or Min
Value:______________
Domain:_______________
Range:________________
Roots:________________
Graph on grid to the right
Use the given information to write the equation of the following quadratics
18. roots: 1, 5 f(7)= -9
19. vertex: (4,-1) f(3) = -6
20. Write the quadratic equation for: Reflect across the x-axis, shrink by ¾, shift down 3 and left 5.
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2nd Quarter Review
PreAP Algebra II
21. Describe the following transformations on the function y = x2:
y = -(x – 1) 2 + 4
22. How is the graph f(x) = (x – 3)2 – 5 obtained from the graph of g(x) = (x + 1)2 – 2?
23. The function g(x) is a translation 4 units right and 6 units down and a vertical stretch of 2 of
f(x) = (x + 3)2 – 2. Write the function g(x).
Give the range for each quadratic.
24. f(x) = 18x2 – 12x – 3
25. f(x) = -(x – 25)2 + 36
26. f(x) = -2(x – 4)(x + 6)
Rewrite the quadratic in translation form by completing the square.
27. f(x) = x2 + 8x + 19
29.
x
f(x)
28. f(x) = 2x2 – 8x + 1
1
9
2
6
3
5
4
6
5
9
6
14
Give the equation in translation form for the quadratic given in the table above.
30. For 1980 through 1990, the average salary, A, (in 1000’s of dollars), of assistant principals at public high
schools can be modeled by A = 2t + 25 where t = 0 represents 1980. Approximate a high school assistant
principal’s salary in 1987.
31. A consultant advises the owners of a beauty salon that their profit p each month can be modeled by
p(x) = -50x2 + 3500x – 2500, where x is the number of customers serviced.
a.) How many customers must be serviced to have a profit of at least $50,000?
b.) What is the maximum profit?
c.) What is the reasonable domain and range for this problem?
32. Falling Object: How long, in seconds, does it take an object dropped from s = 200 feet to strike the
ground? Write your answer rounded to three decimal places. (Hint: the ground is height = 0 and time
cannot be negative)
h(t) = -16t2 + s
33. For the above question, how high would the object be after 1.5 seconds?
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2nd Quarter Review
PreAP Algebra II
34. Maria has a rectangular piece of paper with a perimeter of 38 inches. If she cuts off a 2 inch strip from
the length and cuts off another 2 inch strip from the width, then the length would be exactly 4 times as
long as the width. Write the two equations for the system.
35. For what value of c will the graphs of y = 2x2 – 36x + c and y = 2(x – 9)2 – 18 be the same?
36. The graph of the quadratic function f is shown on the grid below.
What does the solution set for f(x) = 0 appear to be?
A. {12.5}
B. {12.5, -25}
C. {7.5, 17.5}
D. {7.5, 12.5, 17.5}
37. A craftsman wants to spend less than $300 on supplies for making bracelets and necklaces. Supplies for 1
bracelet cost $4, and supplies for 1 necklace cost $9. This relationship is shown in the graph below.
The craftsman wants to make at least 10 more bracelets
than necklaces. Which of the following is a reasonable
solution?
A 25 bracelets and 20 necklaces
B 30 bracelets and 15 necklaces
C 40 bracelets and 20 necklaces
D 15 bracelets and 25 necklaces
38. Which function’s graph has a vertex at (3, 5) and contains the point (5, 13)?
A y=
1
2
( x + 3) − 5
10
C y = 2 ( x − 3) + 5
B y=
1
2
( x − 3) − 5
10
D y = 2 ( x + 3) + 5
2
2
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2nd Quarter Review
PreAP Algebra II
39. An object is launched into the air. The table below shows the objects height above the ground at various
times.
Elapsed Time (sec)
1
2
3
4
5
6
Height Above the
78
109
131
143
145
137
Ground (meters)
Based on the data in the table, what is the object’s height above the ground (to the nearest meter) after 9
seconds after being launched?
40. A quadratic function is graphed on the grid below.
If this function is written in the form y = a(x – h)2 + k, what is the
value of a?
41. Which of the following is a solution to 10x2 – x = 3?
A −
1
5
B
3
5
C −
3
5
D
1
2
42. The function below can be used to model the area of a rectangle in square inches, A, if the rectangle has a
perimeter of 72 inches and a width of w inches.
A = 36w – w2
In this situation, which of the following best describes the domain of the function?
A 0<w<6
B 0 < w < 72
C 0 < w < 18
D 0 < w < 36
43. A table of values for the quadratic function g is shown below.
x
g(x)
-1
-55
2
-16
5
5
6
8
9
5
10
0
12
-16
14
-40
Which of the following statements about the graph of g are true?
I. the graph has a line of symmetry at x = 7
II. the graph has a y-intercept at (0, -40)
III. the graph has an x-intercept at (4, 0)
IV. the graph has a vertext at (6, 8)
A I and II only
B III and IV only
C I, II, and III only
D I, II, III, and IV
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2nd Quarter Review
PreAP Algebra II
44. The roots of a quadratic equation are given by the expression
−25 ± −100
. Which of the following is an
25
equivalent expression?
A −1 ±
2i
5
B −1 ± 2i
C −25 ±
2i
5
D −25 ± 2i
45. The table below shows the values of a quadratic function g.
x
g(x)
-5
-11
-4
8
-3
21
-2
28
-1
29
0
24
1
13
2
-4
3
-27
Based on the table, in which interval can a solution to g(x) = 0 be found?
A -5 < x < -4
B -2 < x < -1
C -1 < x < 1
D 2<x<3
46. What is the solution set for x2 + 4 = 6x?
A
{−3 ± i 14}
B
{−3 ± 5}
C
{3 ± i 14}
D
{3 ± 5}
47. For what value of b will f(x) = x2 + bx + 400 have -20 as its only zero?
48. Which of the following ordered pairs is a solution to the system of inequalities given below?
x+y<4
x2 + y < 8
A (1, 5)
B (1, 2)
C (4, -1)
D (-4, -1)
49. A rectangular parking lot measures 150 ft by 230 ft. The owner of the parking lot will expand the lot’s
size by adding x feet and 2x feet to its dimensions, as shown below.
If the total area of the parking lot cannot exceed 40,000
square feet, which inequality can be used to find all
possible values of x?
A (230 + 2x)(150 + x) < 40,000
B (230 + x)(150 + 2x) < 40,000
C (230 + 2x)(150 + x) > 40,000
D (230 + x)(150 + 2x) > 40,000
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2nd Quarter Review
PreAP Algebra II
50. A function is graphed below.
Which function is best represented by this graph?
A y = -(x + 1)2 + 4
B y = -(x – 1)2 + 4
C y = -x2 + 4x + 3
D y = -x2 – 4x + 3
51.
A factory began producing new parts. Data were
collected on the number of defective parts per 10,000
parts produced. The graph shown to the left displays
some of the data for the first 10 weeks of production.
Based on the graph, during which week were
approximately 130 defective parts per 10,000 produced?
A Week 3
B Week 5
C Week 6
D Week 8
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