algebra 2 worksheet 5.1 name: find the solutions to
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Algebra 2 Worksheet 5.1 Name:________________________
Find the solutions to π π π.
1. π π₯ 4 π₯ 1 π₯ 5 2. π π₯ 2π₯ 10π₯ 3. π π₯ 2π₯ 1 3π₯ 5
4. π π₯ 2.1 π₯ 2.34 π₯ 1 5. π π₯ 3 5π₯ 6 π₯ 7
6. π¦ π₯ 6π₯ 7. π π₯ 3π₯ 27π₯ 8. π¦ 27π₯ 3π₯
9. π π₯ 5π₯ 6π₯ 10. 2π₯ 3 π¦ 11. 20π₯ 5π₯
12. π π₯ 2 π₯ 1 12 13. π¦ π₯ 8π₯ 20 14. 3π₯ 14 2
15. π₯ π₯ 42 16. 4π₯ 37 1 17. π¦ π₯ 6.21π₯
18. π₯ 13π₯ 10 32 19. π₯ 5 84 20 20. π₯ 7π₯ 12
Describe the domain and range of the following functions in interval notation.
21. 22.
23. Given π π₯ 3 π₯ 4 1, identify the name of the parent function and describe how the graph is transformed from the parent function.
A. Quadratic Function with a vertical compression, translated right 4 and up 1 B. Quadratic Function with a vertical stretch, translated right 4 and up 1 C. Linear Function with a vertical compression, translated left 4 and up 1 D. Linear Function with a vertical stretch, translated right 4 and up 1
24. Which equation is obtained after the translation of the graph up 2 units and left 6 units?
A. π π₯ |π₯ 2|
B. π π₯ |π₯| 2
C. π π₯ |π₯ 2|
D. π π₯ |π₯| 2
25. Solve for y: 4 π¦π₯ 2π¦ 3π₯ 4
Algebra 2 Worksheet 5.2 Name:________________________
Find the solutions to π π π.
1. π π₯ π₯ π₯ 3 π₯ 7 2. π π₯ 2 π₯ 3 32 3. π¦ 3π₯ 2 4π₯ 5 π₯ 4
4. π π₯ π₯ 3π₯ 10π₯ 5. π¦ π₯ 6π₯ 40 6. π π₯ π₯ 2π₯ 8π₯
7. π₯ 10π₯ 29π₯ 4π₯ 8. 2π₯ 10π₯ 8π₯ 10. 50π₯ 5π₯
11. π₯ 3 85 4 12. 4π₯ 3π₯ 0 13. 3π₯ 15π₯ 0
14. Which of the following could be the equation for π π₯ ?
A. π π₯ 3 π₯ 1 π₯ 4 π₯ 5
B. π π₯ π₯ 1 π₯ 4 π₯ 5
C. π π₯ π₯ π₯ 1 π₯ 4 π₯ 5
D. π π₯ π₯ π₯ 1 π₯ 4 π₯ 5
15. What is the range of the function π π₯ from #14?
16. Do π π₯ and π π₯ cross the x-axis in the same places? π π₯ π₯ π₯ 15 π₯ 6π π₯ 5π₯ π₯ 15 π₯ 6
17. The graph of π π₯ π₯ is vertically compressed by a factor of and translated to the right three
units and down one unit to produce the function π π₯ . Which of the following equations represents π π₯ ?
A. π π₯
12π₯ 3 1 C. π π₯
12π₯ 3 1
B. π π₯12π₯ 1 3 D. π π₯
12π₯ 1 3
18. Compare the two functions represented below. Determine which of the following statements is true.
Function π π₯ Function π π₯
π π₯ π₯ 6 4
A. The functions have the same vertex.
B. The minimum value of π π₯ is the same as the minimum value of π π₯ .
C. The functions have the same axis of symmetry.
D. The minimum value of π π₯ is less than the minimum value of π π₯ .
Simplify. 19. 2 3π 20. 3 β5 3 β5 21. 5π 6 11π
Algebra 2 Worksheet 5.3 Name:________________________
Find the solutions to π π π.
1. π π₯ 3π₯ 7π₯ 6 2. π π₯ π₯ 10π₯ 9
3. π₯ 85 4 4. 32π₯ 18 π π₯
5. 2π₯ 2π₯ 12 6. π¦ π₯ 2π₯ 1
7. π π₯ 9π₯ 16π₯ 8. π¦ π₯ 36π₯
9. π₯ 2π₯ 14 5π₯ 4 10. 6π₯ 5π₯ 4
11. 10π₯ 6π₯ 4 0 12. 3π₯ 243π₯ 0
13. 3π₯ 18π₯ π π₯ 14. π₯ 81 0
16. Graph the piecewise function.
15. π π₯ π₯ 1 π₯ 5π π₯ π₯ 6π₯ 13
π π₯3 π₯ 2π₯ 1 2 π₯ 3
|π₯ 5| π₯ 3
π. Do π π₯ and π π₯ have the same vertex?
π. Do π π₯ and π π₯ have the same axis of symmetry?
π. Do π π₯ and π π₯ have the same range?
Algebra 2 Worksheet 5.4 Name:________________________
Solve each of the following quadratics using the quadratic formula. Simplify all answers, using π if needed. 1.) π₯ 4π₯ 5 0 2.) π₯ 8π₯ 1 0 3.) π₯ 8π₯ 19 0 4.) 3π 6π 10 5.) 3 8π£ 5π£ 2π£ 6.) 4π₯ 2π₯ 5 7.) The function π π₯ is graphed below. What are the solutions to π π₯ 0?
8.) Graph π π₯ π₯ 8π₯ 15 and give the following information: Hint: probably easiest to convert the equation to y = a(x β h)2 +k form
Vertex:
Min/Max:
y-intercept:
x-intercepts:
9.) The graph of π π₯ π₯ 10π₯ 9 models the height of one of the arches of a doorway, in feet. How wide is the doorway? 10.) What is the height of the doorway at the highest point?
11.) The quadratic equation y = π₯ 10π₯ 21 is shifted left 6 units and down 8 units. What is the new equation, written in vertex form?
Algebra 2 Worksheet 5.5 Name_____________________________________ 1. Use a graphing calculator to solve 2. Draw a sketch: the following system:
π π₯ π₯ 4π₯ 11
π π₯ 3π₯ 4
Solve each system of equations by any method of your choice.
3. π π₯ 3π₯ 9π₯ 3
π π₯ 6π₯ 3 4.
π₯ 4π₯ 3π¦ 6π₯ π¦ 2
5. π π₯ 2π₯ 4π₯ 1
π π₯ π₯ 3 6.
π₯ 6π₯ 8 π¦π¦ 4π₯ 7
7. 6π₯ 27π₯ 3π¦ 108
5π₯ π¦ 6 8.
In the π₯π¦βplane, the parabola with equation π¦ π₯ 11 intersects the line with
equation π¦ 25 at two points, A and B. What is the length of π΄π΅?
9. Solve the system: 10. Solve the system: 11. Use the system of equations below. Which statement best describes the solution set of the system?
π₯ 4π¦ 2
A. The solution set is only the ordered pair (4, 2). B. The solution set is all ordered pairs where x = 4; y can be any real number. C. The solution set is all ordered pairs where y = 2; x can be any real number. D. There is no solution to the system.
12. Which of the following systems of equations could a student use to write a quadratic function in standard form for the parabola passing through the points 1, 4 , 3, 2 , and
2, 17 ?
A. π 4π π π¦
9π 2π π π¦4π 17π π π¦
C. 2π π π 4
6π 3π π 24π 2π π 17
B. π π π 4
9π 3π π 24π 2π π 17
D. π₯ 4π₯ π π¦
3π₯ 2π₯ π π¦2π₯ 17π₯ π π¦
13.) What are the solutions to the quadratic equation, π¦ 2π¦ 9 5π¦ ?
A. π¦
3 3πβ32
C. π¦3 3πβ5
2
B. π¦3 3β5
2 D. π¦
3 3β52
Algebra 2 Unit 5 Practice Test Name:________________________
#1-16: Find the solutions, or zeroes or roots, to each function or equation by using the best method (square rooting,
factoring, or the quadratic formula). Simplify all answers using π if needed.
1.) π₯ 5 41 2.) π₯ 6π₯ 27 0 3.) π₯ 5π₯ 99 3π₯
4.) 4π₯ 18π₯ 4 10π₯ 5.) 2 π₯ 6 45 53 6.) π π₯ 2π₯ 4π₯ 1
7.) 4π₯ 25 0 8.) 3 π₯ 4 18 6 9.) π¦ 2π₯ 9π₯ 4π₯
10.) 3π₯ 5π₯ 3 4π₯ 8 11.) 3π₯ 50 2 12.) π₯ 50π₯ 54 5
13.) 16π₯ 14π₯ 0 14.) 3π₯ 4π₯ 12 15
15.) π₯ 8π₯ 6 3π₯ 16.) 2π₯ 16π₯ 0
17.) The graph of β π₯ π₯ 10π₯ 16 models the height, in feet, of one of the arches at the entrance of a parking structure. What is the width of the parking structure at the base?
18.) Which of following functions does NOT represent the parabola with a vertex at 1, 4 and x-intercepts 1, 0 and 3, 0 .
A. π π₯ π₯ π₯ 4 C. π π₯ π₯ 2π₯ 3
B. π π₯ π₯ 1 4 D. π π₯ π₯ 1 π₯ 3
19.) Compare the axis of symmetry and the minimum values for the two functions below. β π₯ 2 π₯ 3 π₯ 7 π π₯ π₯ 4π₯ 21 Determine which of the following statements is correct.
A. The functions β π₯ and π π₯ have the same axis of symmetry, but the minimum value of β π₯ is less than the minimum value of π π₯ .
B. The functions β π₯ and π π₯ have the same axis of symmetry, but the minimum value of β π₯ is greater than the minimum value of π π₯ .
C. The functions β π₯ and π π₯ do not have the same axis of symmetry, and the minimum value of β π₯ is less than the minimum value of π π₯ .
D. The functions β π₯ and π π₯ do not have the same axis of symmetry, and the minimum value of β π₯ is greater than the minimum value of π π₯ .
20) Write a possible equation for the function graphed below:
Find the solutions for π π₯ 0 in the following functions:
21.) π π₯ 13π₯ 39π₯ 22.) π π₯ 4π₯ 4π₯ 3
For 23-25, find the zeroes.
23.) π₯ 49π₯ 0 24.) π₯ 50 14 25.) 2π₯ 50π₯ 0
Solve each system algebraically:
26.) π π₯ 2π₯ 8π₯ 7π π₯ 4π₯ 7
27.) π π₯ 2π₯ 6π₯ 7π π₯ 5π₯ 5
28.) π₯ 8π₯ 10π¦ 7 19
3π₯ 5π¦ 2
29) Which of the following systems of equations could a student use to write a quadratic function in standard form for the parabola passing through the points (-3, -4), (6, 5) and (-1, 12)?
A. 9π 3π π 436π 6π π 5 π π π 12
C.
9π 4π π π¦36π 5π π π¦ π 12π π π¦
B. 6π 3π π 4
12π 6π π 5 2π π π 12
D.
3π₯ 4π₯ π π¦ 6π₯ 5π₯ π π¦π₯ 12π π π¦