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:

       

    

About the activity

Some outcomes that can be achieved by using this activity include:

  • See how a parabola is uniquely determined by its vertex and just one other point.
  • Equation of parabola in standard and vertex form.
  • See the connection between the exact solutions and the equation in vertex form.
  • Drag the free point to the x-axis so it is a solution, then drag the vertex point to explore the family of parabolas with that solution.
  • Horizontal translation by a corresponds to x → x − a.
  • Vertical translation by b corresponds to y → y − b.
  • Visual demonstration of the fact that all points on a parabola are equidistant from the focus and the directrix.

Interactively study the parabola


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)