This document is an algebra 2 study guide covering various topics involving graphing and solving quadratic functions and equations. It includes:
1) Graphing quadratic functions in standard and vertex form and writing equations between the forms.
2) Solving quadratic equations by factoring, taking square roots, using the quadratic formula, and completing the square.
3) Working with complex numbers including adding, subtracting, multiplying, dividing and finding absolute values.
4) Graphing and solving quadratic inequalities.
Strategic Intervention Material (SIM) was provided for Grade 10 students to enhance learning and to motivate and stir up the attention and interest of the students until they master the topic. This material depicts the entire definition of learning since it concludes a systematic development of students’ comprehension on a distinct lesson in Mathematics 10.
Strategic Intervention Material (SIM) was provided for Grade 10 students to enhance learning and to motivate and stir up the attention and interest of the students until they master the topic. This material depicts the entire definition of learning since it concludes a systematic development of students’ comprehension on a distinct lesson in Mathematics 10.
This presentation is based on the Economic Models, that is the Circular Flow Model and Production Possibility Frontier. It describes about the Production Possibility Curve.
Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
This learner's module will discuss or talk about the Graph of Quadratic Functions. It will also discuss on how to draw the Graph of Quadratic Functions using the vertex, axis of symmetry, etc.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
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This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
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Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
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See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
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The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
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Bob Boule
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https://arxiv.org/abs/2306.08302
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Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
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A2 Chapter 5 Study Guide
1. Algebra 2
Chapter 5 Study Guide
Graphing with Standard Form
Graph the quadratic function and label the vertex.
1. y = 2x2
– 12x + 19 2. y = – 3x2
+ 5
3. y = ½ x2
+ 4x + 5 4. y = – x2
+ 4x – 2
Graphing with Vertex Form
Graph the quadratic function and label the vertex.
5. y = (x – 1)2
+ 2 6. y = – 2(x + 3)2
– 4
7. y = 3(x + 4)2
+ 5 8. y = – 1/3(x + 1)2
+ 3
Write the equation in standard form. Use FOIL.
9. y = (x + 5)(x + 2) 10. y = – (x + 3)(x – 4)
11. y = 2(x – 1)(x – 6) 12. y = – 3(x – 7)(x + 4)
13. y = (x + 3)2
+ 2 14. y = ½ (8x – 1)2
– 3/2
Solving quadratics by factoring. You have to factor first, before you can solve.
Remember the special factoring patterns like using the box, difference of perfect squares
and binomial theorem.
15. x2
– 12x – 28 = 0 16. 3x2
– 17x = - 10
17. 4x2
– 25 = 0 18. 9x2
+ 16 = - 24x
19. 49x2
– 14x = - 1 20. x2
– 48 = 2x
21. 4x2
– 4x – 3 = 0 22. x2
+ 3x – 18 = 0
23. 2x2
– 17x + 45 = 3x – 5
Solving quadratics by square roots.
24. 2x2
+ 1 = 17 25. 2 – 5x2
= - 9
26. 3(x – 2)2
= 21 27. 4x2
– 6 = 42
28. 1/5(x – 4)2
= 6 29. 1/3(x + 5)2
= 7
Complex numbers.
Be able to give examples of Complex Numbers; be able to fill in a diagram.
Be able to plot complex numbers on a grid.
Be able to add and subtract complex numbers.
Be able to multiply and divide complex numbers. Be able to state conjugate of complex
numbers.
Be able to find absolute values of complex numbers.
p. 277 (17 – 71)
Solving by completing the square.
30. x2
+ 10x – 3 = 0 31. 3x2
– 6x + 12 = 0
32. x2
+ 6x – 8 = 0 33. 5x2
– 10x + 30 = 0
34. x2
+ 4x – 1 = 0 35. 3x2
– 12x + 16 = 0
2. Quadratic Formula.
Be able to use the discriminant to tell how many/what kind of solutions a quadratic has.
Be able to use Quadratic Formula (you don’t have to memorize it).
36. 2x2
+ x = 5 37. 3x2
+ 8x = 35
38. 12x – 5 = 2x2
+ 13 39. -2x2
= -2x + 3
40. -x2
+ 2x = 2 41. x2
= 2x – 5
Quadratic Inequalities.
Be able to shade the region given.
Be able to graph systems of quadratic inequalities (more than one).
Be able to solve quadratic inequalities (using the number line and set notation).
Graph:
42. y < 2x2
– 5x – 3 43. y > -x2
– 2x – 3
44. y < -x2
– 4x + 1 45. y > x2
– 4x + 1
46. y < -x2
+ 9 47. y > x2
+ 4x
y > x2
+ 5x – 6 y < 3x2
Solve:
48. x2
– 6x + 5 < 0 49. 2x2
+ 3x – 3 > 0
50. -x2
– 9x + 36 > 0 51. -3x2
+ x + 7 < 0
