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Graphing Quadratic Functions and Understanding Probability: Easy Steps for Kids

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~Taffi~

6/28/2023

Algebra 1

Quadratic formula notes

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Algebra 1

Graphing Quadratic Functions and Understanding Probability: Easy Steps for Kids

A comprehensive guide to mathematical concepts covering graphing quadratic functions step by step, probability theory, and mutually exclusive events explained with examples.

  • Quadratic functions are explored through both standard form (y=ax²+bx+c) and vertex form (y=a(x-h)²+k), with emphasis on graphing techniques and key features
  • Probability concepts are thoroughly explained, covering basic probability calculations, dependent and independent events, and conditional probability
  • The relationship between events is detailed through mutually exclusive events and their probability calculations
  • Visual aids and practical examples are used throughout to reinforce mathematical concepts
  • Special attention is given to probability constraints and real-world applications
...

6/28/2023

192

|y=ax ² +bx+c Standard form * Make a table, or use the table function on the calculator. TIP - a will tell where the 29 you 'vertex is! Exam

View

Page 2: Introduction to Probability

This page covers the fundamental concepts of probability and its basic calculations. The content explains how probability is calculated and interpreted in various scenarios.

Definition: Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Example: The probability of getting heads when flipping a coin is 1/2 or 50%.

Vocabulary: A constraint is defined as a condition or equation that limits possible outcomes.

Highlight: Probability values always range between 0 and 1, with 1 representing certainty and 0 representing impossibility.

|y=ax ² +bx+c Standard form * Make a table, or use the table function on the calculator. TIP - a will tell where the 29 you 'vertex is! Exam

View

Page 3: Applied Probability Problems

This page demonstrates practical applications of probability concepts through various examples and calculations.

Example: A problem involving a circle with circumference 36π containing a smaller circle, calculating the probability of a random point lying in the smaller circle.

Highlight: The solution involves calculating areas and using the ratio of areas to determine probability.

Definition: Intuitive probability refers to understanding likelihood through logical reasoning rather than formal calculations.

|y=ax ² +bx+c Standard form * Make a table, or use the table function on the calculator. TIP - a will tell where the 29 you 'vertex is! Exam

View

Page 4: Dependent and Independent Events

This page explores the relationship between events and their probability calculations, focusing on dependent and independent events.

Definition: Independent events are those where the outcome of one event does not affect the probability of another event.

Example: "Picking two sweets from a bag with replacement" demonstrates independent events, while "picking without replacement" shows dependent events.

Highlight: For independent events, PA∩BA∩B = PAA×PBB, while for dependent events, PA∩BA∩B = PAA×PB∣AB|A.

|y=ax ² +bx+c Standard form * Make a table, or use the table function on the calculator. TIP - a will tell where the 29 you 'vertex is! Exam

View

Page 5: Mutually Exclusive Events

This page explains the concept of mutually exclusive events and their probability calculations.

Definition: Mutually exclusive events are events that cannot occur simultaneously.

Example: When spinning a coin twice, getting heads and tails on the same spin is mutually exclusive.

Highlight: For mutually exclusive events, PA∩BA∩B=0 and PA∪BA∪B=PAA+PBB.

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Subjects

Algebra 1

 

Algebra 1

•

192

•

Jun 28, 2023

•

5 pages

Graphing Quadratic Functions and Understanding Probability: Easy Steps for Kids

user profile picture

~Taffi~

@taffi

A comprehensive guide to mathematical concepts covering graphing quadratic functions step by step, probability theory, and mutually exclusive events explained with examples.

  • Quadratic functions are explored through both standard form (y=ax²+bx+c) and vertex form (y=a(x-h)²+k), with emphasis on... Show more

|y=ax ² +bx+c Standard form * Make a table, or use the table function on the calculator. TIP - a will tell where the 29 you 'vertex is! Exam

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Page 2: Introduction to Probability

This page covers the fundamental concepts of probability and its basic calculations. The content explains how probability is calculated and interpreted in various scenarios.

Definition: Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Example: The probability of getting heads when flipping a coin is 1/2 or 50%.

Vocabulary: A constraint is defined as a condition or equation that limits possible outcomes.

Highlight: Probability values always range between 0 and 1, with 1 representing certainty and 0 representing impossibility.

|y=ax ² +bx+c Standard form * Make a table, or use the table function on the calculator. TIP - a will tell where the 29 you 'vertex is! Exam

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Applied Probability Problems

This page demonstrates practical applications of probability concepts through various examples and calculations.

Example: A problem involving a circle with circumference 36π containing a smaller circle, calculating the probability of a random point lying in the smaller circle.

Highlight: The solution involves calculating areas and using the ratio of areas to determine probability.

Definition: Intuitive probability refers to understanding likelihood through logical reasoning rather than formal calculations.

|y=ax ² +bx+c Standard form * Make a table, or use the table function on the calculator. TIP - a will tell where the 29 you 'vertex is! Exam

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Dependent and Independent Events

This page explores the relationship between events and their probability calculations, focusing on dependent and independent events.

Definition: Independent events are those where the outcome of one event does not affect the probability of another event.

Example: "Picking two sweets from a bag with replacement" demonstrates independent events, while "picking without replacement" shows dependent events.

Highlight: For independent events, PA∩BA∩B = PAA×PBB, while for dependent events, PA∩BA∩B = PAA×PB∣AB|A.

|y=ax ² +bx+c Standard form * Make a table, or use the table function on the calculator. TIP - a will tell where the 29 you 'vertex is! Exam

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 5: Mutually Exclusive Events

This page explains the concept of mutually exclusive events and their probability calculations.

Definition: Mutually exclusive events are events that cannot occur simultaneously.

Example: When spinning a coin twice, getting heads and tails on the same spin is mutually exclusive.

Highlight: For mutually exclusive events, PA∩BA∩B=0 and PA∪BA∪B=PAA+PBB.

|y=ax ² +bx+c Standard form * Make a table, or use the table function on the calculator. TIP - a will tell where the 29 you 'vertex is! Exam

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Graphing Quadratic Functions

This page introduces the fundamental concepts of quadratic functions and their graphical representations. The content focuses on two main forms of quadratic equations and their characteristics.

Definition: A quadratic function can be written in either standard form y=ax2+bx+cy=ax²+bx+c or vertex form y=a(x−hy=a(x-h²+k).

Vocabulary: Key terms include domain, range, roots alsocalledzeroesorx−interceptsalso called zeroes or x-intercepts, axis of symmetry, and vertex.

Example: For the function y=2x+3x+3²-1, the vertex is at −3,−1-3,-1 with a=2 indicating upward opening parabola.

Highlight: The coefficient 'a' determines the direction and steepness of the parabola - positive 'a' opens upward, negative 'a' opens downward.

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I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

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Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

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In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user