Polynomials
Name: _________________________
Write each polynomial in standard form. Then name each expression by its degree and number of terms.
1. −3𝑥 + 4 + 6𝑥 2
By Degree
By Terms
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_________________
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2. 5𝑥 + 7𝑥 3
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Simplify each expression and write the answer in standard form.
3. (−4𝑥 3 − 8𝑥 2 + 3𝑥) − (−6𝑥 3 + 3𝑥 2 − 9𝑥)
4. 3𝑡(2𝑡 − 4𝑡 2 ) + 𝑡(−2𝑡 + 3𝑡 2 )
Find each product. Write in standard form.
5. 5x(x  3)
6. 4x 2 (x  7)
7. (3x  5)(2x  1)
8. (x  6)(x  6)
9. (x  2)(2x 2  x  4)
10. (2𝑥– 7)2
11. x 2  8x  15
12. x 2  25
13. 4𝑥 2 + 12𝑥 + 9
14. 3x 2  14x  8
15. 2x 2  5x  3
16. 4x2 + 36x
17. 2𝑥 3 − 8𝑥 2 + 5𝑥 − 20
18. 5𝑥 3 − 25𝑥 2 − 2𝑥 + 10
19. 5𝑐 2 − 125
Factor each expression completely.
20. Sam uses one-inch frames for pictures for which the length is 4 inches (in.) longer than the width. Draw a picture.
The area of the frame for a picture that is x inches wide is given by the expression:
(𝑥 + 2)(𝑥 + 6) − 𝑥(𝑥 + 4)
There are four descriptions shown. Place the correct expression to the appropriate box below the corresponding
description.
𝑥
(𝑥 + 6)
𝑥(𝑥 + 4)
(𝑥 + 2)(𝑥 + 6)
The length of the
picture alone, in
inches
a)
The length of the
frame, in inches
(𝑥 + 4)
The area of the picture
alone, in square inches
The area of the
picture and the frame
together , in square
inches
Find the area of the frame in standard form.
Quadratic Functions
Name the zeroes of the following quadratic functions.
21. 𝑓(𝑥) = (𝑥 − 4)(𝑥 + 3)
22. 𝑓(𝑥) = 𝑥(𝑥 − 5)
Find the zeroes of the quadratic functions by factoring.
23. 𝑓(𝑥) = 𝑥 2 + 7𝑥 − 30
24. 𝑓(𝑛) = 6𝑥 2 − 5𝑥 − 4
25. 𝑓(𝑥) = 𝑥 2 + 18𝑥 + 80
Graph the following quadratic functions: Be sure to find the VERTEX, LINE OF SYMMETRY, Y-INTERCEPT, ZEROS.
26. 𝑓(𝑥) = 𝑥 2 − 8𝑥 + 12
27. 𝑓(𝑥) = 2𝑥 2 − 4𝑥
28. Sketch a graph that models the following situation. Label intercepts and maximum or minimum
Brad is practicing his football field goal skills. He kicks the ball from the ground. After 2.4
seconds, the ball goes reaches its maximum height of 30 feet. After 4.8
seconds, the ball hits the ground.
29. Given the following quadratic function: 𝒚 = 𝒙𝟐 + 𝟒𝒙 − 𝟒
a) Write the equation in vertex form by completing the square.
b) Find the maximum or minimum point (vertex)
of the given quadratic function
c) Find the axis of symmetry
d) Sketch the graph (above)
30. Find the zeroes of the quadratic function by factoring: 6𝑥 2 − 7𝑥 – 3 = 0
31. Find the zeroes of the quadratic function by completing the square: 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 2
32. A basketball player is shooting a free throw. The data in the table models the height of the ball after
release. The resulting data is shown below.
Choose the function that best models the situation.
1
1
a. 𝑦 = 2 𝑥 + 4
b. 𝑦 = − 2 𝑥 2 + 4𝑥 + 4
1
c. 𝑦 = 2 − 4𝑥
d. 𝑦 = |𝑥| + 4
33. Solve each equation by finding square roots. If the equation has no solution write no solution.
a. 9x2 – 16 = 0
b. x2 + 9 = 0
34. Find the value of n such that 𝑥 2 + 24𝑥 + 𝑛 is a perfect square trinomial.
The graph shows the height of a soccer ball over 5 seconds.
35. Describe the situation which best represents the graph.
36. Answer following questions, using the graph above.
a) Identify the x intercepts and explain what they represent in this context.
b) Does this graph have a maximum or does it have a minimum? Give the coordinates of this point.
c) Where is the function increasing?
d) Where is the function decreasing?
37. Evel Knievel was attempting to jump 4 cars on his motorcycle. His jump off a 3 meter ramp gave him a
maximum height of 4 meters after 2 seconds. Here is the resulting data:
a) Choose the function that best models the situation
a) y = 4x
b) y = -x + 4
c) 𝑦 = −𝑥 2 + 4𝑥
Time (seconds)
0
1
2
3
4
Height (meters)
0
3
4
3
0
38. Solve for x using the quadratic formula. 𝑥 =
a) 2𝑥 2 − 6𝑥 − 4 = 0
b) Find the height of Evel Knievel at 2.5 seconds.
−𝑏±√𝑏 2 −4𝑎𝑐
2𝑎
b) 6𝑥 2 + 7𝑥 + 2 = 0
Exponential Functions
Given the graph of each function, find the y-intercept and state the domain and range.
40. 𝑦 = 2 ∙ 2x
1 𝑥
41. 𝑦 = −3 ∙ (3)
y-intercept:
y-intercept:
x-intercept:
x-intercept:
growth or decay factor:
growth of decay factor:
Does it grow or decay?
Graph each exponential function.
1 𝑥
43. 𝑦 = 4 ∙ 2𝑥
42. 𝑦 = 2 ∙ (2)
Determine if the following tables represent linear or exponential functions. Write the model that represents
the given table.
44.
1
2
3
4
45.
For problems 46- 48 write an equation for each situation.
-2
y = a ● (1 + r)x or
46. A colony of mice starts with 5 mice and grows by 20% each year.
47. You invest $12,000 at a bank that pays an annual interest rate of 12%.
48. You buy a tractor for $500. Its value depreciates by 15% each year.
-1
0
y = a ● (1 – r)x
1
49. Mr. Sennett has a deer population of 200 on his family farm. For the last 3 months, one-half of the deer
population has died each month due to disease.
a) Will this data be best represented by a linear or exponential model? Explain your reasoning.
b) Complete the table and make a graph to represent the growth over time.
Month
Total Deer
0
1
2
3
c) What is the slope or growth factor?
What does it represent in the context
of the problem?
d) What is the y-intercept for this
relationship? What does it represent
in the context of the problem?
e) Choose the equation the best represents the situation.
1 𝑥
1) 𝑦 = 200 ∙ (2)
1
2) 𝑦 = 2 ∙ (200)𝑥
1
3) 𝑦 = 200𝑥 + 2
Statistics
1
4) 𝑦 = 2 𝑥 + 200
Exam
Scores
80
50. Using the table, create a box plots for exam scores
a. Write the data in order from least to greatest.
90
75
b. Find the range of the given data.
80
90
c. Find the Lower, Middle and Upper Quartiles
d. Create the box plot in the space provided below.
85
65
95
51. On the grid provided, create a scatterplot of the data.
X Values
1
3
4
6
6
7
8
11
12
14
a.
Y Values
61
60
59
59
58
57
56
56
54
53
Draw a line of best fit through the data.
b. Describe the correlation.
c. Find the equation of your line of best fit.
Radicals
Simplify each radical expression.
52.
12  27
56.
86 2
53.
3 50
57. 6√27 + 3√12
54.
180
55.
9

58. 6 7  3 3

6
3
59. (√2 + 3)2
Rational Expressions
Simplify the given rational expressions:
60.
62.
61.
63.