targas-edu.de
DE ☾ A+

Shifting parabolas

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

You shift the standard parabola up, down, right and left. You learn the vertex form \(y = a \cdot (x - d)^2 + e\).
📄 Open worksheet (PDF, German)

The video

In the video the vertex moves. You see where the parabola slides.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Up and down
  2. 0:31 Right and left
  3. 0:57 The vertex form
  4. 1:33 Careful, mistake!
  5. 1:57 Try it yourself

The most important points

Up and down

\(y = x^2 + 2\): Every \(y\)-value becomes 2 bigger. The parabola slides 2 up, \(S(0|2)\). \(y = x^2 - 3\): 3 down, \(S(0|-3)\).

The standard parabola shifted up and down.
The standard parabola shifted up and down.

Right and left

\(y = (x - 2)^2\): The bracket is zero for \(x = 2\). The parabola goes 2 to the right, \(S(2|0)\). \(y = (x + 3)^2\): 3 to the left, \(S(-3|0)\).

Shifted to the right and to the left.
Shifted to the right and to the left.

Vertex form

\(y = a \cdot (x - d)^2 + e\) has the vertex \(S(d|e)\) (die Scheitelpunktform). Examples: \(y = (x - 2)^2 + 1\) has \(S(2|1)\). \(y = -(x + 1)^2 + 3\) has \(S(-1|3)\) and is open downwards (\(a < 0\)).

Two parabolas with their vertex.
Two parabolas with their vertex.

Careful: \(y = (x + 3)^2\) goes to the left, not to the right. The vertex is where the bracket is zero: \(x + 3 = 0\), so \(x = -3\).

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/3
The worksheet – Page 2
Page 2/3
Show the worksheet solutions
The worksheet – Page 3
Page 3/3

Try it yourself

Task

Give the vertex of \(y = (x + 1)^2 - 2\). Is the parabola open upwards or downwards?

Show solution

\(S(-1|-2)\). \(a = 1\): open upwards.

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Parabeln verschieben und die Scheitelpunktform y = a·(x − d)² + e. Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.