Properties (characteristics) of parabolas

A parabola is the graph of a quadratic equation/function. It an be either in the shape of the letter 'U' or it can be in the shape of the inverted letter of 'U'.

There are three main characteristics of a parabola. These are:

  1. Vertex: The point at the apex of a parabola.
  2. x-intercepts: The point/s at which the parabola intersects or touches the x-axis.
  3. Focus
  4. Directrix
  5. Axis
  6. Ordinate/Double ordinate
  7. Latus Rectum
  8. Face: If the parabola is in the form of the letter 'U', then its face is upwards. If the parabola is the in form of the inverted letter 'U', then its face is downwards.
Based on the above characteristics, there can be six different kinds of parabolas:

No x-intercepts: The parabola does not meet the x axis:
One x-intercept: The parabola touches the x-axis at one point:

Two x-intercepts: The parabola intersects the x-axis at two points:

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