Graphing Quadratics

Graphing Quadratics Screenshot  Download  Embed
  • Graphing
  • Parabola
  • Quadratic Function
Flash Logo Original Sim and Translations


  • Graphing
  • Parabola
  • Quadratic Function
  • Vertex


Discover how changing coefficients changes the shape of a curve. View the graphs of individual terms (e.g. y=bx) to see how they add to generate the polynomial curve. Generate definitions for vertex, roots, and axis of symmetry. Compare different forms of a quadratic function. Define a curve by its focus and directrix.

Sample Learning Goals

  • Describe how changing the coefficients of a quadratic function changes the graph of the function.
  • Predict how the graph of a parabola will change if the coefficients or constant are varied.
  • Identify the vertex, axis of symmetry, roots, and directrix for the graph of a quadratic equation.
  • Use the vertex form of a quadratic function to describe the graph of the function.
  • Describe the relationship between the focus and directrix and resulting parabola.
  • Predict the graph of a parabola given a focus and directrix.

Standards Alignment

Common Core - Math

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
Graph linear and quadratic functions and show intercepts, maxima, and minima.
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
Derive the equation of a parabola given a focus and directrix.
Version 1.1.5

Teacher Tips

Download teacher tips PDF Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

Teacher-Submitted Activities

Parabolas on the Move! A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Lauren Rider, Alayna Vuylsteke HS
Quadratic Transformations (Vertex form) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Jennifer Moeller, Kevin Stirling HS Guided Mathematics
Mapping of PhET and IBDP Physics Jaya Ramchandani HS Other Physics
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) This contribution was designed by PhET. Diana López HS
Other Physics
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) This contribution was designed by PhET. Diana López HS
Other Mathematics
Uma Proposta de Estudo de Pontos de Máximo e Mínimo de uma Função Quadrática Emanuel Viana HS
Lab Mathematics
Função Quadrática aplicada ao OA "Gráfico de Quadráticas" Renata Passos Machado Vieira e Francisco Regis Vieira Alves HS Other
Parabola walter Manuel Trujillo Yaipen Grad
Lab Mathematics
Gráficando Rectas, Gráficando Cuadráticas Andrés Gualberto Palomo Cuevas HS HW

Language Download or Run Tips
Albanian All shqip Download Run now Paraqitja grafike e funksioneve katrore
Arabic All العربية Download Run now رسم معادلات الدرجة الثانية
Basque All Euskara Download Run now Kuadratikoak marrazten
Bosnian All Bosanski Download Run now Grafik kvadratne funkcije
Chinese (Simplified) All 中文 (中国) Download Run now 二次函数图像
Chinese (Traditional) All 中文 (台灣) Download Run now Graphing Quadratics_繪製二次曲線
Danish All Dansk Download Run now Tegning af andengrads-ligninger
Dutch All Nederlands Download Run now Kwadratische grafieken
French All français Download Run now Graphiques quadratiques 
German All Deutsch Download Run now Quadratische Kurven
Greek All Ελληνικά Download Run now Γραφικές αναπαραστάσεις δευτεροβάθμιων εξισώσεων
Hindi All हिंदी Download Run now द्विघात का आलेख 
Hungarian All magyar Download Run now Másodfokú polinomrajzoló
Italian All italiano Download Run now Rappresentazione grafica di Quadratiche
Japanese All 日本語 Download Run now 二次方程式のグラフ
Kazakh All Kazakh Download Run now Квадрат функция графигі
Korean All 한국어 Download Run now 2차 방정식 그래프 그리기
Latvian All Latviešu Download Run now Kvadrātvienādojumu zīmēšana
Mongolian All Монгол (Монгол) Download Run now Квадрат Функцын График
Persian All فارسی Download Run now رسم معادلات درجه دو
Polish All polski Download Run now Wykresy funkcji kwadratowych
Portuguese (Brazil) All português (Brasil) Download Run now Gráfico de Quadráticas
Russian All русский Download Run now График квадратичной функции
Serbian All Српски Download Run now График квадратне функције
Slovak All Slovenčina Download Run now Grafy kvadratických funkcií
Spanish All español Download Run now Graficando Cuadráticas Download teacher tips PDF
Spanish (Mexico) All español (México) Download Run now Graficando Cuadráticas  Download teacher tips PDF
Spanish (Peru) All español (Perú) Download Run now Graficando Cuadráticas
Swedish All svenska Download Run now Plotta Andragradsekvationer
Tamil All Tamil Download Run now பரவளையி வரைபு
Turkish All Türkçe Download Run now İkinci Dereceden Denklem Grafikleri
Ukrainian All українська Download Run now Графік квадратичної функції Download teacher tips PDF
Vietnamese All Tiếng Việt Download Run now Đồ thị hàm bậc 2

HTML5 sims can run on iPads and Chromebooks, as well as PC, Mac, and Linux systems.

iOS 12+ Safari
iPad compatible sims

Not officially supported. If you are using the HTML5 sims on Android, we recommend using the latest version of Google Chrome.

Latest version of Google Chrome
The HTML5 and Flash PhET sims are supported on all Chromebooks.
Chromebook compatible sims

Windows Systems:
Microsoft Edge, latest version of Firefox, latest version of Google Chrome.

Macintosh Systems:
macOS 10.13+, Safari 13+, latest version of Chrome.

Linux Systems:
Not officially supported. Please contact with troubleshooting issues.

Design Team Third-party Libraries Thanks To
  • Chris Malley (developer)
  • Andrea Lin (developer)
  • Amanda McGarry (lead designer)
  • Michael Dubson (original designer)
  • Karina K. R. Hensberry
  • Trish Loeblein
  • Ariel Paul
  • Kathy Perkins
  • almond-0.2.9.js
  • base64-js-1.2.0.js
  • FileSaver-b8054a2.js
  • font-awesome-4.5.0
  • game-up-camera-1.0.0.js
  • he-1.1.1.js
  • himalaya-0.2.7.js
  • jama-1.0.2
  • jquery-2.1.0.js
  • lodash-4.17.4.js
  • pegjs-0.7.0.js
  • seedrandom-2.4.2.js
  • text-2.0.12.js
  • TextEncoderLite-3c9f6f0.js