•

Dec 12, 2025

•

2 pages

Understanding Parabola Transformations

Edna B.

@dna._zvcl

Quadratic functions show up everywhere in math and real life,... Show more

# Transforming Quadratic Functions: Intro to Parabola
# Transformations

Algebra 1

## Basic Quadratic Function:

- A basic quadratic functi

Introduction to Parabola Transformations

The simplest quadratic function is f(x) = x², which creates a U-shaped curve called a parabola with its vertex at (0,0). This basic parabola serves as our starting point before applying any transformations.

You can change this basic parabola's position, size, and orientation through different transformations. When moving a parabola horizontally, we use f $x - h$ or f $x + h$ — if h is positive, the graph shifts right; if h is negative, it shifts left. For vertical movements, we use f(x) + k or f(x) - k — positive k moves the graph up, while negative k moves it down.

Reflection is another key transformation that flips the parabola. When you write -f(x), you're reflecting the parabola about the x-axis, turning the U-shape upside-down into an upside-down U.

💡 Think of transformations like dressing up your parabola! Horizontal shifts move it side to side, vertical shifts move it up and down, and reflections flip it over like a pancake.

Advanced Parabola Transformations

Dilation changes how steep or flat your parabola appears. When you write af(x) where a is positive, you're stretching or compressing the parabola vertically. If a > 1, the parabola stretches taller and narrower; if 0 < a < 1, it becomes shorter and wider.

You can combine multiple transformations to create more complex parabolas. When working with multiple changes, follow this order: reflect first, then dilate, and finally shift. Keeping this sequence helps you accurately predict how the final graph will look.

For example, the function f(x) = 2 $x - 3$ ² + 4 combines three transformations. The parabola is stretched vertically by a factor of 2, shifted 3 units right, and moved 4 units up from the original position. Drawing these transformations step-by-step helps visualize the final result.

🔑 When analyzing a transformed quadratic function, break it down into pieces! Identify each transformation separately $stretch/compression, horizontal shift, vertical shift$ before putting them back together.

We thought you’d never ask...

What is the Knowunity AI companion?

Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.

Where can I download the Knowunity app?

You can download the app in the Google Play Store and in the Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

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

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

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

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

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

Elisha

iOS user

Paul T

iOS user

Algebra 1

•

Dec 12, 2025

•

2 pages

Understanding Parabola Transformations

Edna B.

@dna._zvcl

Quadratic functions show up everywhere in math and real life, from the path of a soccer ball to the shape of satellite dishes. When we transform these functions, we can shift, stretch, or flip their U-shaped graphs (parabolas) to model... Show more

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

Introduction to Parabola Transformations

Reflection is another key transformation that flips the parabola. When you write -f(x), you're reflecting the parabola about the x-axis, turning the U-shape upside-down into an upside-down U.

💡 Think of transformations like dressing up your parabola! Horizontal shifts move it side to side, vertical shifts move it up and down, and reflections flip it over like a pancake.

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

Advanced Parabola Transformations

🔑 When analyzing a transformed quadratic function, break it down into pieces! Identify each transformation separately $stretch/compression, horizontal shift, vertical shift$ before putting them back together.