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This discussion is about the relationship between parabolas and quadratic functions. Quadratic functions are here.

Definition: Let d be a line (the directrix) and F be a point (the focus) not on d.

A parabola is all the points C such that the length of \overline{CF} equals the distance from C to d.

If the directrix is a horizontal line, the parabola is a quadratic function.

Click and drag the point Q along d to trace the parabola. Move F along the y-axis to change the focus. (Here, the focus F is restricted to a point on the y-axis and the directrix d is set so that the vertex of the parabola is always (0,0).)

Why this construction?

I did not even know what a directrix was.(Without really thinking about it, I guess I assumed that a parabola was the graph of a quadratic function and not vice-versa.)Related topics: