Study parabolas in the number plane. Consider regions where the quadratic expression is positive, negative, or zero. and relate them to the equation of the parabola. Consider symmetry, and explore the effect of translation. Compare the two forms of the equation of a parabola.

Parabola Explorer
Investigate their shape, equations and other properties

Adjust the constraints and drag the points to explore the graphs and equations of a variety of parabolas.

Standard form:
Vertex form:
Solution:

## Interactively study the parabola

• Drag the vertex or other point (each shown in blue).
• The change in the parabola then depends on the constraint setting:
• None
The vertex and point may be dragged anywhere, redefining the parabola,
X
The x coordinate of the vertex and point are fixed, so they can only be dragged up or down,
Y
The y coordinate of the vertex and point are fixed, so they can only be dragged left or right,
X + Y
The point moves only along the arms of the current parabola, and moving the vertex moves the parabola correspondingly.
• If Show Focus is selected, the focus and directrix are shown in green, as well as line-segments showing the associated (equal) distances.
• Values are shown as fractions or decimals according to the state of the Fractions setting.
• The equation of the current parabola is constantly displayed and updated as points are moved. Alternatively it can be entered using the Enter equation… dialog in either standard form, i.e. y = 2x^2 - 4x - 5 or vertex form, i.e. (x - 1)^2 = 1/2 (y + 7).
• Click and hold the chart background to bring up a magnifier.

Enter an equation for a parabola:

Use either standard or vertex form,
e.g. y = 2x^2 - 4x - 5 or (x - 1)^2 = 1/2 (y + 7)