Quadratic Relations


Basic Information About Quadratic Relations

More Information About Quadratic Relations (b ≠ 0)

More Information About Quadratic Relations (b = 0)

Relating Quadratic Relations to Physical Models (Conic Sections)


How to Use this Applet

Definitions

Slider Definitions

  • <SHIFT>+drag: Hold down the <SHIFT> key, then drag the described object.
  • <CTRL>+drag: Hold down the <CTRL> key, then drag the described object.
  • <CTRL>+<SHIFT>+drag: Hold down both the <CTRL> key and the <SHIFT> key, then drag the described object.

The Slider Area

The sliders change the parameters A, B, C, D, E and F in the quadratic relation y = Ax² + Bxy + Cy² + Dx + Ey + F = 0.

  • Select the "A", "B", "C", "D", "E" or "F" buttons or press the "A", "B", "C", "D", "E" or "F" keys to change to the selected parameter/slider.
  • The <LEFT> and <RIGHT> arrow keys can also be used to change the selected parameter/slider.
  • Drag the slider thumb to change the value of a parameter. Use the <UP> and <DOWN> arrow keys to increase or decrease the selected parameter. (Use the keys for fine adjustments.)
  • NOTE: If a key doesn't respond:
    • position the cursor in the applet frame
    • click the mouse button
    • try the key again.
  • Drag a slider scale to change the range of the scale while maintaining the scale length.
  • Drag a location in a slider gutter towards or away from the thumb to change both the range of the scale and the scale length.
  • Select the corresponding parameter button to enter a value for a parameter.

The Graph Area

  • <SHIFT>+drag in the graph area to move the entire coordinate system.
  • <CONTROL>+drag in the graph area, towards or away from:
    • the x-axis, to change the y-axis scale.
    • the y-axis, to change the x-axis scale.

Other

  • Select the RESET button to restore the applet to the initial state.