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Desmos Graphing: Easy Parabolas and Quadratic Equations for Kids!

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Diallo

2/13/2023

Algebra 2

8.2 Graph and write equations of parabolas

Desmos Graphing: Easy Parabolas and Quadratic Equations for Kids!

This parabola opens upward with vertex at (0, 0) and focus at (0, 2). The directrix is y = -2. The equation is x² = 8y.

...

2/13/2023

394

Vertex (0;0)
directrix
X=
x= op
X z 4 py ; p > 0
Vertex
(0;0)
Focus
(0;P)
2
y z 4 px
→
directrix V=-P
j
8.2
Formula
focus (P;0),
pro
Ventex

View

Understanding Parabola Equations

This page introduces the fundamental components of parabolas and their equations. It covers both vertically and horizontally oriented parabolas, emphasizing the relationship between the equation form and the parabola's orientation.

For vertically oriented parabolas yaxissymmetryy-axis symmetry, the standard form is x² = 4py, where p determines the distance from the vertex to the focus and directrix. The focus is located at 0,p0, p and the directrix at y = -p.

For horizontally oriented parabolas xaxissymmetryx-axis symmetry, the equation takes the form y² = 4px. Here, the focus is at p,0p, 0 and the directrix is x = -p.

Vocabulary: Vertex - The point where a parabola changes direction, often the highest or lowest point.

Definition: Directrix - A line perpendicular to the axis of symmetry of a parabola, used in defining the parabola.

Highlight: The value of p in the equation determines whether the parabola opens upward/rightward p>0p > 0 or downward/leftward p<0p < 0.

The page also presents variations of these equations for parabolas with different orientations and openings, providing a comprehensive overview of parabola equation forms.

Vertex (0;0)
directrix
X=
x= op
X z 4 py ; p > 0
Vertex
(0;0)
Focus
(0;P)
2
y z 4 px
→
directrix V=-P
j
8.2
Formula
focus (P;0),
pro
Ventex

View

Deriving Parabola Equations from Graphs

This page demonstrates how to derive a parabola equation from a given graph or set of information. It presents an example of a horizontally oriented parabola.

The example shows a parabola with its vertex at 0,00, 0 and focus at 2,0-2, 0. The directrix is located at x = 2.

Example: For a parabola with focus at 2,0-2, 0 and directrix at x = 2, the equation is derived as y² = -8x.

The process of deriving the equation involves:

  1. Identifying the orientation of the parabola horizontalinthiscasehorizontal in this case.
  2. Locating the focus and directrix.
  3. Applying the general formula y² = 4px, where p is the distance from the vertex to the focus.
  4. Calculating p as -2 negativebecausetheparabolaopenstotheleftnegative because the parabola opens to the left.

Highlight: The axis of symmetry for this parabola is y = 0, which is consistent with its horizontal orientation.

This example illustrates the practical application of parabola equation formulas and demonstrates how to use a parabola graph calculator conceptually.

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Algebra 2

394

Feb 13, 2023

3 pages

Desmos Graphing: Easy Parabolas and Quadratic Equations for Kids!

This parabola opens upward with vertex at (0, 0) and focus at (0, 2). The directrix is y = -2. The equation is x² = 8y.

Vertex (0;0)
directrix
X=
x= op
X z 4 py ; p > 0
Vertex
(0;0)
Focus
(0;P)
2
y z 4 px
→
directrix V=-P
j
8.2
Formula
focus (P;0),
pro
Ventex

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Understanding Parabola Equations

This page introduces the fundamental components of parabolas and their equations. It covers both vertically and horizontally oriented parabolas, emphasizing the relationship between the equation form and the parabola's orientation.

For vertically oriented parabolas yaxissymmetryy-axis symmetry, the standard form is x² = 4py, where p determines the distance from the vertex to the focus and directrix. The focus is located at 0,p0, p and the directrix at y = -p.

For horizontally oriented parabolas xaxissymmetryx-axis symmetry, the equation takes the form y² = 4px. Here, the focus is at p,0p, 0 and the directrix is x = -p.

Vocabulary: Vertex - The point where a parabola changes direction, often the highest or lowest point.

Definition: Directrix - A line perpendicular to the axis of symmetry of a parabola, used in defining the parabola.

Highlight: The value of p in the equation determines whether the parabola opens upward/rightward p>0p > 0 or downward/leftward p<0p < 0.

The page also presents variations of these equations for parabolas with different orientations and openings, providing a comprehensive overview of parabola equation forms.

Vertex (0;0)
directrix
X=
x= op
X z 4 py ; p > 0
Vertex
(0;0)
Focus
(0;P)
2
y z 4 px
→
directrix V=-P
j
8.2
Formula
focus (P;0),
pro
Ventex

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

Deriving Parabola Equations from Graphs

This page demonstrates how to derive a parabola equation from a given graph or set of information. It presents an example of a horizontally oriented parabola.

The example shows a parabola with its vertex at 0,00, 0 and focus at 2,0-2, 0. The directrix is located at x = 2.

Example: For a parabola with focus at 2,0-2, 0 and directrix at x = 2, the equation is derived as y² = -8x.

The process of deriving the equation involves:

  1. Identifying the orientation of the parabola horizontalinthiscasehorizontal in this case.
  2. Locating the focus and directrix.
  3. Applying the general formula y² = 4px, where p is the distance from the vertex to the focus.
  4. Calculating p as -2 negativebecausetheparabolaopenstotheleftnegative because the parabola opens to the left.

Highlight: The axis of symmetry for this parabola is y = 0, which is consistent with its horizontal orientation.

This example illustrates the practical application of parabola equation formulas and demonstrates how to use a parabola graph calculator conceptually.

Vertex (0;0)
directrix
X=
x= op
X z 4 py ; p > 0
Vertex
(0;0)
Focus
(0;P)
2
y z 4 px
→
directrix V=-P
j
8.2
Formula
focus (P;0),
pro
Ventex

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

Quadratics and parabolas are fundamental concepts in algebra, with wide-ranging applications in mathematics and physics. This guide provides a comprehensive overview of parabola equations, focusing on their key components and how to derive them from graphs.

  • The guide covers different forms of parabola equations, including those with vertical and horizontal axes of symmetry.
  • It explains crucial elements such as the vertex, focus, and directrix of parabolas.
  • Examples are provided to illustrate how to write parabola equations from given information or graphs.
  • The relationship between the focus, directrix, and the equation of a parabola is thoroughly explored.

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Paul T

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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